The UK Biobank project is a prospective cohort study with deep genetic and phenotypic data collected on approximately 500,000 individuals from across the United Kingdom, aged between 40 and 69 at recruitment. The open resource is unique in its size and scope. A rich variety of phenotypic and health-related information is available on each participant, including biological measurements, lifestyle indicators, biomarkers in blood and urine, and imaging of the body and brain. Follow-up information is provided by linking health and medical records. Genome-wide genotype data have been collected on all participants, providing many opportunities for the discovery of new genetic associations and the genetic bases of complex traits. Here we describe the centralized analysis of the genetic data, including genotype quality, properties of population structure and relatedness of the genetic data, and efficient phasing and genotype imputation that increases the number of testable variants to around 96 million. Classical allelic variation at 11 human leukocyte antigen genes was imputed, resulting in the recovery of signals with known associations between human leukocyte antigen alleles and many diseases. Deep phenotype and genome-wide genetic data from 500,000 individuals from the UK Biobank, describing population structure and relatedness in the cohort, and imputation to increase the number of testable variants to 96 million. As such, a key component of the UK Biobank resource has been the collection of genome-wide genetic data on every participant using a purpose-designed genotyping array2. An interim release of genotype data on approximately 150,000 UK Biobank participants in May 20153 has already facilitated numerous studies6.Understanding the role that genetics has in phenotypic and disease variation, and its potential interactions with other factors, is crucial for a better understanding of human biology. It is hoped that this will lead to more successful drug developmentIn this paper, we summarize the existing and planned content of the phenotype resource and describe the genetic dataset on the full 500,000 participants. To facilitate its wider use, we applied a range of quality control procedures and conducted a set of analyses that reveal properties of the genetic data—such as population structure and relatedness—that can be important for downstream analyses. In addition, we estimated haplotypes and imputed genotypes into the dataset that increases the number of testable variants by more than 100-fold to approximately 96 million variants. We also imputed classical allelic variation at 11 human leukocyte antigen (HLA) genes, and replicated signals of known associations between HLA alleles and many common diseases. We describe tools that allow efficient genome-wide association studies (GWAS) of multiple traits and fast phenome-wide association studies, which work together with a new compressed file format that has been used to distribute the dataset. As a further check of the genotyped and imputed datasets, we performed a test-case genome-wide association scan on a well-studied human trait, standing height.7. Once recruitment was fully underway, further enhancements were introduced to the assessment visit, including a range of eye measures, an electrocardiograph test, arterial stiffness and a hearing test.A wide variety of phenotypic information as well as biological samples have been collected for each of the approximately 500,000 UK Biobank participants Fig. . At recr8 with repeated measures being collected over a period of a year  from 2,500 of these participants. A multi-modal imaging assessment is currently underway, which comprises magnetic resonance imaging (MRI) of the brain9, heart10 and body, carotid ultrasound11 and a whole body dual-energy X-ray absorptiometry of the bones and joints12. Data collection started in 2014 and is anticipated to take 7–8 years to achieve imaging for 100,000 participants in dedicated imaging assessment centres across the United Kingdom, with repeat imaging measures being planned for a subset of participants.The baseline information has been, and will continue to be, extended in several ways. For example, repeat assessments are planned to be conducted in subsets of the cohort every few years, to enable calibration of measurements, adjustment for regression dilution, and estimation of longitudinal change. Objective measures of physical activity have also been collected  in 100,000 participants in 2013–201413.All participants provided consent for follow-up through linkage to their health-related records. As of May 2018, there were over 14,000 deaths, 79,000 participants with cancer diagnoses, and 400,000 participants with at least one hospital admission. Considerable efforts are now underway to incorporate data from a range of other national datasets including primary care, screening programmes, and disease-specific registries, as well as asking participants directly about health-related outcomes through online questionnaires (see Extended Data Table 1c for diabetes and rheumatoid factor for arthritis), or the ability to characterize phenotypes not otherwise well assessed .Measurements for a wide range of biochemical markers of key interest to the research community have also been carried out, including those that have known associations with disease , diagnostic value  that shares 95% of marker content with the UK BiLEVE Axiom Array. The marker content of the UK Biobank Axiom array was chosen to capture genome-wide genetic variation (single nucleotide polymorphism (SNPs) and short insertions and deletions (indels)), and is summarized in Fig. 2.The UK Biobank genetic data contains genotypes for 488,377 participants. These were assayed using two very similar genotyping arrays. A subset of 49,950 participants involved in the UK Biobank Lung Exome Variant Evaluation (UK BiLEVE) study were genotyped at 807,411 markers using the Applied Biosystems UK BiLEVE Axiom Array by Affymetrix (now part of Thermo Fisher Scientific), which is described elsewhereDNA was extracted from stored blood samples that had been collected from participants on their visit to a UK Biobank assessment centre. Genotyping was carried out by Affymetrix Research Services Laboratory in 106 sequential batches of approximately 4,700 samples see . Affymet14. Although most (94%) individuals report their ethnic background as within the broad-level group ‘white’, there are still approximately 22,000 individuals with a self-reported ethnic background originating outside Europe , and provide this list to researchers.To identify poor quality markers, we used statistical tests designed primarily to check for consistency across experimental factors, such as array or batch see . As a re16, can be used as a way to detect possible sample mishandling or other types of clerical error. In a dataset of this size, some such mismatches would be expected due to transgender or intersex individuals, or instances of rare genetic variation, such as sex-chromosome aneuploidies17. Using information in the measured intensities of chromosomes X and Y . A small number of markers (around 300) have very different allele frequencies (see Supplementary Information section r2 = 0.93) , especially for rare markers.More than 110,000 rare markers (MAF < 0.01 in UK Biobank) were included on the two arrays used for the UK Biobank cohort19. We used PCA to measure population structure within the UK Biobank cohort  among UK Biobank participants were not recorded during the collection of other phenotypic information. This information can be important for epidemiological analysesoser see . A totaloser see . This isoser see . The larPairs of related individuals within the UK Biobank cohort form networks of related individuals. In most cases, these are of size two, but there are also many groups of size three or larger in the cohort Fig. , even whThere are 172 family groups with 5 or more individuals that are second-degree relatives or closer Fig. . One suc23. For the pre-phasing step, we only used markers present on both the UK BiLEVE and UK Biobank Axiom arrays. We removed markers that failed quality control in more than one batch, had a greater than 5% overall missing rate, and had a MAF of less than 0.0001. We removed samples that were identified as outliers for heterozygosity and missing rate. These filters resulted in a dataset with 670,739 autosomal markers in 487,442 samples. Phasing on the autosomes was carried out using SHAPEIT324 (see https://jmarchini.org/software/). The 1000 Genomes phase 3 dataset25 was used as a reference panel, predominantly to help with the phasing of samples with non-European ancestry. In a separate experiment that leveraged phase inferred from mother–father–child trios, we estimated a median phasing switch error rate of 0.229% (see We estimated haplotypes for the full cohort (pre-phasing), followed by haploid imputation229% see .26 data as the main imputation reference panel because it consisted of the largest available set  of broadly European haplotypes at 39,235,157 SNPs. Supplementary Fig. We used the Haplotype Reference Consortium (HRC)27, which has 87,696,888 bi-allelic markers. We combined this imputed data with that from the HRC panel, using the HRC imputation when a SNP was present in both panels. Imputation was carried out with the IMPUTE4 program (https://jmarchini.org/software/), which is a re-coded version of the haploid imputation functionality implemented in IMPUTE223 (see http://hgdownload.cse.ucsc.edu/goldenpath/hg19/database/).We also imputed the UK Biobank using the merged UK10K and 1000 Genomes phase 3 reference panelsE223 see . The resα in a sample of M individuals indicates that the amount of data at the imputed marker is approximately equivalent to a set of perfectly observed genotype data in a sample size of αM. The figure illustrates that most markers above 0.1% frequency have high information scores. Previous GWAS have tended to use a filter on information around 0.3 that roughly corresponds to an effective sample size of approximately 150,000. Thus, it may be possible to reduce the information score threshold and still obtain good power to detect associations.Extended Data Fig. http://www.well.ox.ac.uk/~gav/bgen_format/bgen_format.html) and software library  to provide improved data compression, the ability to store phased haplotype data and random access to the data via use of a separate index file. Using this new format, the full imputed files require 2.1 Tb of file space. A new program  was built using the BGEN library to carry out fast multi-trait GWAS and phenome-wide association studies28  resolution for 11 classical HLA genes  using the HLA*IMP:02 algorithm with a multi-population reference panel  on chromosome six is the most polymorphic region of the human genome and contains the largest number of genetic associations to common diseasesloci see , 8.31. Here we observed evidence of association and effect size estimates for HLA alleles that are concordant in direction and relative magnitude with those found in the IMSGC study, although in 11 out of 14 cases this was closer to 1, consistent with regression dilution bias arising from a low rate of phenotypic error  in the UK Biobank but not in the GIANT study  in both GIANT and the UK Biobank imputed data  and the Oxford Brain Imaging Genetics server28 (http://big.stats.ox.ac.uk/). We anticipate that the availability of the full genetic data for UK Biobank will result in a further step change in this productive research cycle. The UK Biobank is a powerful example of the immense value that can be achieved from large population scale studies that combine genetics with extensive and deep phenotyping and linkage to health records coupled with a strong data sharing policy. It is likely to herald a new era in which these and related resources drive and enhance understanding of human biology and disease.The interim release of the genetic data on approximately 150,000 participants in UK Biobank has already facilitated many papers exploring the links between human genetic variation and disease, and their connection with a wide range of environmental and lifestyle factors. The UK Biobank continues to grow with the addition of further phenotypic information and as researchers return the results of their analyses for UK Biobank to share. Online resources are being developed for sharing the results of analyses using UK Biobank data, including the release of GWAS results for thousands of phenotypes . Blood samples were collected from participants on their visit to a UK Biobank assessment centre and the samples are stored at the UK Biobank facility in Stockport, UK25. Genotypes were then called from the array intensity data, in units called ‘batches’ which consist of multiple plates. Across the entire cohort, there were 106 batches of 4,700 UK Biobank samples each .On receipt of DNA samples, Affymetrix processed samples on the GeneTitan Multi-Channel (MC) Instrument in 96-well plates containing 94 UK Biobank samples and two control samples from the 1000 Genomes Projectles each . Followi36, and genotype calling37. Any sample that did not pass these checks was excluded from the resulting genotype calls. The custom-designed arrays contain a number of markers that had not been previously typed using Affymetrix genotype array technology. As such, Affymetrix also applied a series of checks to determine whether the genotyping assay for a given marker was successful, either within a single batch, or across all samples. Where these newly attempted assays were not successful, Affymetrix excluded the markers from the data delivery  genetic variation, such as sex-chromosome aneuploidies17. Affymetrix genotype calling on the X and Y chromosomes allows only haploid or diploid genotype calls, depending on the inferred sex16. Therefore, cases of full or mosaic sex chromosome aneuploidies may result in compromised genotype calls on all, or parts of, the sex chromosomes (but not affect the autosomes). For example, individuals with karyotype XXY will probably have poorer quality genotype calls on the pseudo-autosomal region (PAR) of the X chromosome, as they are effectively triploid in this region. Using information in the measured intensities of chromosomes X and Y, we identified a set of 652 (0.134%) individuals with sex chromosome karyotypes putatively different from XY or XX  that we identified as sample duplicates  for approximately 150,000 UK Biobank participants improvements were made to the genotype calling algorithm5 for app38) that performs well on datasets with hundreds of thousands of samples by approximating only the top n principal components that explain the most variation, in which n is specified in advance. We computed the top 40 principal components using a set of 407,219 unrelated, high quality samples and 147,604 high quality markers pruned to minimise linkage disequilibrium39. We then computed the corresponding principal component-loadings and projected all samples onto the principal components, thus forming a set of principal component scores for all samples in the cohort . Our PCA revealed population structure even within this category  and it is implemented in an algorithm efficient enough to consider all pairs (~1.2 × 1011) in a practicable amount of time. As noted by the authors of KING, we found that recent admixture  tended to inflate the estimate of the kinship coefficient, as the estimator assumes Hardy–Weinberg equilibrium among markers with the same underlying allele frequencies within an individual. We alleviated this effect by only using a subset of markers that are only weakly informative of ancestral background  and confirmed 100% of the twins, parent-offspring and sibling pairs, and 99.9% of pairs overall  using a different inference method implemented in PLINK .Haplotype estimation (phasing) was carried out using SHAPEIT3 in chunks of 15,000 markers, with an overlap of 250 markers between chunks. Each chunk used 4 cores per job and 43. Investigations on the effect of sample size on phasing performance and downstream imputation performance suggest that differences between methods will have negligible effect on genotype imputation and GWAS42.We assessed the accuracy of the phasing in a separate experiment by taking advantage of mother-father-child trios that were identified in the UK Biobank cohort. This family information can be used to infer the phase of a large number of markers in the trio parents. These family-inferred haplotypes were used as a truth set, as is common in the phasing literature. The parents of each trio were removed from the dataset and then haplotypes were estimated across chromosome 20 in a single run of SHAPEIT3. This dataset consisted of 16,175 autosomal markers. The inferred haplotypes were then compared to the truth set using the switch error metric. Using a set of 696 trios with self-reported ethnic background ‘British’ (within the broader-level group ‘white’) and no other twins or first- or second-degree relatives in the UK Biobank dataset, we estimated a median switch error rate of 0.229%. We also used a subset of 397 of these trios that also had no third-degree relatives and obtained a median switch error rate of 0.234%. These error rates are similar to those produced by other phasing methods that can handle data at this scale23 to focus exclusively on the haploid imputation needed when samples have been pre-phased. This new version of the program is referred to as IMPUTE4 (see https://jmarchini.org/software/), but uses exactly the same hidden Markov model within IMPUTE2, and produces identical results to IMPUTE2 when run using all reference haplotypes as hidden states (data not shown). To reduce RAM usage and increase speed we use compact data structures that store the indices of haplotypes carrying the non-reference allele at variant sites in the reference panel. Not only is this data structure compact, but at each stage of the forward-backward algorithm it also allows the calculations involving the emission part of the hidden Markov model to sum only over just the subset of haplotypes that carrying the non-reference allele in an efficient way. A further increase in speed is obtained by only calculating the marginal copying probabilities at those sites common to the target and reference datasets, and then linearly interpolating these for SNPs in-between those sites that need to be imputed. Imputation was carried out in chunks of approximately 50,000 imputed markers with a 250 kb buffer region and on 5,000 samples per compute job. The combined processing time per sample for the whole genome was approximately 10 min.To facilitate fast imputation of all 500,000 samples, we re-coded IMPUTE2For haplotype estimation on the X chromosome genotype data we applied the same filtering steps as the autosomal genotype data, with some additional filters. For both the sex-specific region and the pseudo-autosomal regions (PAR), samples were excluded which were identified as having a likely sex chromosome aneuploidy (see above). For the PAR, we additionally excluded samples with a missing rate of >5% among markers in the PAR. For the sex-specific region of chromosome X, this resulted in a dataset of 16,601 markers and 486,790 samples. For the PAR this resulted in a dataset of 1,239 markers and 486,476 samples. Haplotype estimation and genotype imputation was carried out on the two pseudo-autosomal regions and the non-pseudo autosomal region separately, and using the same methods and reference datasets used for the autosomes.31) for HLA alleles and each disease using logistic regression. The risk model , as described previously31, was used to enable comparison of effect size estimates. For validation and further details, see Supplementary Information section SP > 2.40 × 10−4, the Bonferroni corrected level of association) with any HLA alleles, which is consistent with the lack of associations in the HLA region in recent analyses of each phenotype45For each individual we defined the HLA genotype at each locus as the pair of alleles with maximum posterior probability as reported by HLA*IMP:02. We performed association analysis  imputation was carried out on them; (ii) in the white British ancestry subset (see above); and (iii) the inferred sex matches the self-reported sex. From this group we selected a set of 344,397 unrelated individuals . For sta46 to look for evidence of statistical association between each marker and standing height. We report association statistics based on a linear mixed model (BOLT-LMM-inf), with the following covariates: (i) array (UK BiLEVE Axiom Array or UK Biobank Axiom Array); (ii) sex (inferred); (iii) age when attended UK Biobank assessment centre; and (iv) principal components 1–20.We used the software BOLT-LMM (v2.2)The principal components scores were computed using only individuals within the white British ancestry subset, but otherwise with the same method as described above. We conducted tests using the genotype and imputed data files separately.r2) between markers in this region show a pattern that is as expected in the context of linkage disequilibrium, and the local recombination rates. The stripe-like pattern of the association statistics is indicative of multiple mutations occurring on similar branches of the genealogical tree underlying the data, which are probably linked to varying degrees with the causal marker(s). The correlation between the most associated marker and all other markers in the region drops off sharply around the small peak in recombination47 to the right of the most significantly associated marker. Notably, this marker was imputed from the genotypes, which points to the success of the imputation in this study, and in general, to the value of imputing millions more markers. Human height is a highly polygenic trait, so provided an opportunity to examine many such regions of association, and other regions that we visually examined showed similar patterns.Extended Data Fig. For Fig. 33 and summarize the results in Extended Data Fig. For a given phenotype, the 95% credible set in a region of association is the smallest set of markers that together have 95% posterior probability of containing the marker causally associated with the phenotype. We found credible sets for standing height using the method described previously15  after regressing out the covariates used in the GWAS. We then confirmed that the effect size estimates for overlapping markers were comparable between the two studies.For each marker in each study, we computed a Bayes factor in favour of association with standing height using the effect sizes and standard errors, and 0.2i drives the association signal in the region r is given by:kr is the Bayes factor for marker i in the r region33. The 95% credible set for a region is found by going down the list of markers ordered from highest to lowest posterior probability and stopping when the cumulative posterior reaches 0.95.If there is exactly one causal marker in the region and genotypes for that marker are available in the data, then the posterior probability that a marker 2) and much larger prior (202). We found that overall the choice of prior had little effect on the results. Specifically for values we report in the main text, the median credible set sizes were unaffected in all analyses. For the larger prior, the number of single-marker credible sets was unaffected except for analysis B in UK Biobank (from 123 to 122), and the median proportion of markers in the credible set was unaffected in all analyses. For the smaller prior, the number of single-marker credible sets only changed for analysis A, going from 78 to 75 in GIANT, and 85 to 86 in UK Biobank, and the median proportion of markers in the credible set increased slightly in all analyses (maximum increase from 0.047 to 0.051).We assessed the sensitivity of our results to the choice of prior by conducting the same analyses using a much smaller prior (0.02https://jmarchini.org/software/. This software is licensed free for use by researchers at academic institutions. The BGEN library source code is available at https://bitbucket.org/gavinband/bgen. BGENIE is built using this library. Pre-compiled binaries for the latest version of BGENIE are available at https://jmarchini.org/software/. This software is currently licensed free for use by researchers at academic institutions. Commercial organizations wishing to use IMPUTE4 or BGENIE must enquire about a licence from the University of Oxford.Genotype imputation was carried out using IMPUTE4.0. Pre-compiled binaries for the latest version of IMPUTE4 are available at Further information on research design is available in the Any methods, additional references, Nature Research reporting summaries, source data, statements of data availability and associated accession codes are available at 10.1038/s41586-018-0579-z.Supplementary InformationThis file contains Supplementary Material, including Supplementary Figures S1-S18 and Supplementary Tables S1-S13.Reporting Summary


The United States Department of Agriculture (USDA) National Plant Germplasm System (NPGS) sorghum core collection contains 3011 accessions randomly selected from 77 countries. Genomic and phenotypic characterization of this core collection is necessary to encourage and facilitate its utilization in breeding programs and to improve conservation efforts. In this study, we examined the genome sequences of 318 accessions belonging to the NPGS Sudan sorghum core set, and characterized their agronomic traits and anthracnose resistance response.We identified 183,144 single nucleotide polymorphisms (SNPs) located within or in proximity of 25,124 annotated genes using the genotyping-by-sequencing (GBS) approach. The core collection was genetically highly diverse, with an average pairwise genetic distance of 0.76 among accessions. Population structure and cluster analysis revealed five ancestral populations within the Sudan core set, with moderate to high level of genetic differentiation. In total, 171 accessions (54%) were assigned to one of these populations, which covered 96% of the total genomic variation. Genome scan based on Tajima’s D values revealed two populations under balancing selection. Phenotypic analysis showed differences in agronomic traits among the populations, suggesting that these populations belong to different ecogeographical regions. A total of 55 accessions were resistant to anthracnose; these accessions could represent multiple resistance sources. Genome-wide association study based on fixed and random model Circulating Probability (farmCPU) identified genomic regions associated with plant height, flowering time, panicle length and diameter, and anthracnose resistance response. Integrated analysis of the Sudan core set and sorghum association panel indicated that a large portion of the genetic variation in the Sudan core set might be present in breeding programs but remains unexploited within some clusters of accessions.The NPGS Sudan core collection comprises genetically and phenotypically diverse germplasm with multiple anthracnose resistance sources. Population genomic analysis could be used to improve screening efforts and identify the most valuable germplasm for breeding programs. The new GBS data set generated in this study represents a novel genomic resource for plant breeders interested in mining the genetic diversity of the NPGS sorghum collection. Germplasm collections are an important genetic resource used by plant breeders for the development of new crop varieties that are better adapted to different agricultural systems worldwide. Because germplasm collections are large in size, management of these collections for the maintenance of genetic diversity and identification of desired traits or cultivars is a complex task. In fact, there exists a large gap between the genetic diversity present in the germplasm collection and that used in plant breeding programs . To encoSorghum bicolor (L.) Moench] is a highly diverse cereal crop composed of five botanical races  characterized by different inflorescence types because of multiple domestication events  G.W. Wilson), is a prevalent disease in warm and humid sorghum cultivation regions. In highly susceptible lines, anthracnose can cause substantial yield losses (up to 50%) of both grain and biomass , flanking the causal gene Sobic.006G147400  locus, which determines the midrib color in sorghum, as shown recently by GWAS and biparental mapping . LogistiThe GWAS for FL found association with two genomic regions in chromosome 1 and 4. Both genomic regions account for up to 28% of the observed variation. The region in chromosome 4 explains 20% of the observed variation and is constituted by 30 kb block with four genes (Sobic.004G155600 – Sobic.004G155900). These genes are annotated as encoding heat shock proteins, ribonucleoprotein, acetolactate synthase and uncharacterized proteins. The associated SNP in chromosome 1 was located 200 bp downstream of gene (Sobic.001G512633) encoding an uncharacterized protein.Dw2 dwarfing gene located in the 42.8 Mb region [The GWAS for PH found association with seven genomic regions located in chromosome 1 and 6 . Each of these genome regions explains 1–4% of the observed variation, however, together account for up to 18%. Two genomic regions in chromosome 6 were 315 kb upstream and 3.19 Mb downstream from the b region .The GWAS for PL found association with two genomic regions in chromosome 4 and one genomic region in chromosome 6. One genomic region in chromosome 4 explains 28% of the observed variation and is constituted by the SNP S4_49996017 located 3.5 kb upstream of the gene Sobic04G157700. This gene encodes the cell wall hydroxyproline-rich glycoprotein. The genomic region in chromosome 6 explains 11% of the observed variation and is constituted by the SNP S6_46298267 located within the gene Sobic06G093000. This gene encodes a methyltransferase.The GWAS for PD found association with seven genomic regions located in chromosomes 5 and 6. Each of these genome regions explains 1–7% of the observed variation, and together account for up to 25%. The 14.31 kb genomic region in chromosome 6 explains 7% of the variation and enclose three genes (Sobic06G095100 – Sobic06G095300). Functional annotation of these genes includes OBPS-3-responsive proteins, microsomal signal peptidase and uncharacterized proteins.The GWAS for anthracnose resistance found association with four genomic regions located in chromosome 2 and 5. Each genomic region in chromosome 2 explains 2% of the observed variation. The SNP S2_6699292 is located within the gene Sobic02G067600 that encode an RNA recognition motif. The other two genomic regions in chromosome 2, SNPs S2_53789238 and S2_66061610, are in two intergenic regions of 189 and 6 kb, respectively. The genomic region in chromosome 5 (SNP S5_651137569) explains 7% of the observed variation and is in a 6 kb intergenic region.The NPGS sorghum collection is an important public germplasm resource for sorghum breeders and the scientific community worldwide. Nevertheless, screening of this large collection for economically important traits is challenging, expensive, and requires high-throughput phenotyping techniques. Moreover, the photoperiod sensitivity of most of the germplasm limits the screening to tropical regions, where plants can flower under short days. Today, most of the genetic diversity of NPGS collection remains untapped, while most of the improved varieties are genetically related because of inbreeding, and are therefore vulnerable to abiotic and biotic stresses. Understand the phenotypic and genetic diversity that exists among and within germplasm collection enables development of adequate strategies for breeding and allele mining .Core collections are developed as germplasm resources for the screening and identification of valuable accessions . NeverthPreserve most of the allelic diversity present in a germplasm collection is necessary for the security of agriculture . The sucTan1 gene  suggests that each population may contain different anthracnose resistance sources. The GWAS identified four loci that might be related to Sudan population structure. We observed allelic variation for the SNP S2_6699313 is limited to populations 2 and 5. Likewise, the genetic variation for the SNP S2_53789238 is limited to population 5, while genetic variation for SNP S2_66061610 is observed in populations 1, 2, 3 and 4. The genetic variation of the SNP in chromosome 5 (S5_65137569) is limited to population 3 and 5. These genomic regions explain a limited portion of the observed variation indicating the presence of other loci. Indeed, 11 resistance accessions could not be associated with these four resistance loci. The statistical power of GWAS for the detection of rare alleles (MAF < 0.05) is very low and decreases further when multiple rare alleles underlying similar phenotypes are present in the selected panel [In Sudan, sorghum is mostly cultivated in drought-prone areas , where eme 5 S5_637569 is ed panel –55. ThisThe fifty-five Sudanese anthracnose resistance accessions identify herein could be used increase the genetic diversity of breeding programs. Phylogenetic analysis showed these resistance accessions represent the genetic variation in the Sudan core collection  were planted at the research farms of the USDA-Agricultural Research Service (ARS) Tropical (18°28′18.6″N 67°02′37.1″W) and Mayaguez (18°12′41.5″N 67°08′08.0″W), Puerto Rico, during the short day-length season  in 2014 and 2016, respectively. A completely randomized design was used at both locations, with plots measuring 1.8 m in length and with 0.9 m spacing between rows. Plants were maintained using standard management practices. Weeds were controlled by mechanical tillage and hand hoeing, and aerial watering (Raingun Irrigation) was applied in the absence of rainfall.Proc mixed covtest procedure of SAS , where location and accessions were considered fixed effects. Performances of accessions were estimated based on least square means. Midrib color was classified as white, green, and green-yellow at maturity.Flowering time (FL), plant height (PH), panicle length (PL), panicle diamter (PD), PL/PD ratio, and midrib color were recorded for each plot at both locations. FL was defined as the number of days until 50% of the plants within a plot reached anthesis. PH referred to the average distance from the base of the main stalk at the soil level to the top of the panicle of three plants per plot at maturity. PL and PD referred to the distance from the first rachis to the top of the panicle and the widest section of the panicle, respectively . Data frHigh relative humidity (> 80%) at both locations was conducive for the development of anthracnose disease and the evaluation of disease resistance. Five previously characterized pathotypes from Isabela  and threProc mixed covtest procedure of SAS. The location and accession were considered fixed effects, and blocks were treated as random effects. Anthracnose resistance response was estimated based on least square mean.Sixty-six accessions resistant to anthracnose at both locations were evaluated in triplicate for one additional year (2017) together with reference checks at Isabela, Puerto Rico, in a randomized complete block design consisting of three blocks of 1.8 m long plots with 0.9 m spacing between rows. Data of the three experiments were combined to perform ANOVA using the ApeKI restriction enzyme, and the data were deposited at the National Center for Biotechnology Information (NCBI) Sequence Read Archive (SRA) database. To determine the genetic variation among accessions, genomic DNA was isolated from a pool of five seedlings, as described previously  using bowtie2 [plants.ensembl.org; accessed April 2019).The Sudan core collection was subjected to GBS  using th-Drouard , and re- bowtie2 , while t bowtie2  was used bowtie2 , as implGenomic information of 342 accessions from the SAP was obtained from the NCBI SRA database . Sequences of all 660 accessions (342 accessions in the SAP and 318 accessions in the Sudan core set) were aligned against the BTx623 sorghum genome v.3 using bowtie2 . Raw seqr2 < 0.10) was generated using PLINK [k value set from 1 to 13 were performed using STRUCTUE. The ad hoc statistic Δk based on the rate of change in the log probability of data between successive k values [A pruned subset of 5366 unlinked SNPs  [The number of private SNPs was estimated among accessions in the Sudan core collection and SAP  and amonST)  among thST) . Tajima’ST) . PairwisST) . The resST) .The GWAS was conducted based on the phenotypic data of FL, PH, PL, PD, PL/PD ratio, and anthracnose resistance with the fixed and random model Circulating Probability (farmCPU) model using the GAPPIT package  in the Rblock function was used to delimited genomic regions related to associated SNPs. Log quantile-quantile (QQ) p-value plots were examined to determine how well farmCPU and logistic regression accounted for population structure and family relatedness. Manhattan and QQ plots were visualized using the R package qqman [The PLINK  block fuge qqman .p = 0.01 as implemented in GAPPIT. The empirical significance threshold for logistic regressions with the midrib data using the Sudan core set  was calculated with 1000 permutations for an experiment-wise error rate of p = 0.05.Empirical significance thresholds for farmCPU were based on Bonferroni with experiment-wise error rate of Additional file 1: Table S1. List of sorghum accessions from the USDA-NPGS Sudanese core collection. Table S2. Hierarchical organization of the genetic relatedness of 318 accessions from the USDA-NPGS Sudan germplasm collection based on the population structure analysis of 5000 unlinked SNPs. Table S3. Anthracnose resistance response and agronomic traits of USDA-NPGS Sudan sorghum core collectionAdditional file 2: Figure. S1. Genome-wide association study (GWAS) of midrib color in the NPGS Sudan core collection. (A) Manhattan plot for logistic regression based on case-control analaysis , and significance threshold of p-values < 0.05 and < 0.001 based on 1000 permutations. (B) Log quantile-quantile (Q-Q) p-value plotsAdditional file 3: Figure. S2. Log quantile-quantile (Q-Q) p-value plots for the genome-wide association study (GWAS) of plant height, panicle length and diameter, flowering time and anthracnose resistance in the NPGS Sudan core collection. GWAS based on the fixed and radom model Circulating Probability Unification (farmCPU) regression analysisAdditional file 4: Figure. S3. Unrooted neighbor-joining tree of 55 anthracnose resistance accessions present in NPGS Sudan core collection based on the analysis of 5366 unlinked SNPs. Colored branches represent accessions belonging to the five population present in the core collection and admixture accessions are not colored


Gossypium hirsutum L.) recombinant inbred line (RIL) mapping population that was evaluated under contrasting irrigation treatments, well-watered and water-limited conditions, in a hot, arid environment in 2012. Two phenotypic data sets were used in combination with the genetic data which consisted of 841 marker loci assigned to 117 linkage groups. The first dataset contained canopy traits that were gathered using a mobile, high-throughput phenotyping platform and included canopy temperature (CT), normalized difference vegetation index (NDVI), and canopy height (CHT) with leaf area index (LAI) being derived from NDVI and CHT measurements. The second phenotypic data set consisted of 14 elemental concentration measurements corresponding to the following elements: P, K, Ca, Mn, Fe, Zn, Ni, Cu, As, Co, Rb, Mo, S, and Mg. To conduct the PSLR analyses we used the “pls” and “pls depot” available in R statistical software version 3.2.4. The PLSR bi plot from the analysis of the first dataset showed that three  out of the four canopy traits were highly correlated, and by using multivariate analysis of variance (MANOVA), we detected 22 significant (p<0.01) marker-trait associations for the four traits. In contrast to the canopy trait analysis, our PLSR bi plot for the second dataset showed varying correlations for each of the 14 traits. Because of the lack of distinct trait similarities, MANOVA was not an ideal option to test for marker-trait associations so we implemented a jackknife re sampling technique. Jackknife re sampling failed to detect significant marker effects for several of the 14 elemental concentration traits. Thus, our future work aims to test other re sampling techniques such as boot straping for traits that do not exhibit high correlation. Overall, PLSR was a very informative way to comprehend data structure, displaying correlations within markers, within traits, and between marker and traits in one bi plot. Further studies are still needed to leverage detection of additional variance in correlated datasets and to prevent spurious results. To the best of our knowledge, this is the first time PLSR has been reported in such a context.In this work, we investigated the suitability of performing partial least square regression (PLSR) on genotype-phenotype datasets to identify marker-trait associations. We utilized data collected on a cotton ( Although many quantitative traits that are measured on populations exhibit moderate to high correlations, standard marker-trait association methods are univariate and thus unable to capitalize on this trait relatedness. A common approach to handling this situation so that standard univariate approaches can be used is to create a composite score that combines the measurements of multiple traits into one. However, the analysis of these composite scores is known to entail loss of statistical power .Aiming to improve complex marker-trait association studies and to contribute to a better understanding of correlated datasets, we performed partial least square regression (PLSR) in two drought-related cotton phenotypic datasets. To the best of our knowledge, this is the first time PLSR has been reported in such context.PLSR was first proposed to solve the multi collinearity problem in regression or calibration ,3. In thIn PLSR, X and Y are projected into new spaces. The projection matrices are named T and U, respectively. P and Q are the orthogonal loading matrices for X and Y, respectively . ThroughIn our work, we used markers as predictors, X, and traits as the responses variable, Y, to find the multidimensional direction in the X space that explained the maximum multidimensional variance direction in the Y space. Through the construction of a bi plot, correlations within markers, within traits, and between markers and traits, can all be detected and displayed .PLSR was performed on two cotton datasets that were collected during 2012 at the University of Arizona’s Maricopa Agricultural Center (MAC) in Maricopa, AZ. Phenotypic data were collected on 95 recombinant inbred lines (RILs) from the TM-1×NM24016 bi parental mapping population ,8 evaluaThe first dataset analyzed contained three traits that were directly measured on the cotton canopy using a mobile, high-throughput phenotyping platform which has been previously described . These cThe second dataset analyzed for this work is a set of 14 elemental concentrations measured on the seeds of the RIL population evaluated in 2012. The elements assayed for this work include P, K, Ca, Mn, Fe, Zn, Ni, Cu, As, Co, Rb, Mo, S, and Mg. All the data collection and univariate association tests were conducted and published by [Data processing of the phenotypic measurements was performed in both datasets using a differential between the well-watered and the water-limited treatments. The idea of a trait differential was to have only one measurement for each of the traits analyzed to avoid having to conduct separated multivariate analyses for each irrigation treatment. For instance, if a plant reaches a canopy height of 10 cm if well-watered, and of 6 cm if water-limited due to drought-stress, we would use the difference in growth of 4 cm as the differential phenotype in Y.Marker-trait association studies in plants are generally conducted using quantitative trait loci (QTL) analyses. QTL software that are currently available can use multiple markers, however they can only use one trait at the time. Our goal was to use all the traits and all the markers in one analysis.In this work, we propose using PLSR as a multivariate tool due to the simultaneous correlations input and the increase power. Further more, its bi plot offers a great graphical display of all the data to aid researchers in decision-making processes. For the first dataset with four drought-related traits we performed PLSR as well as a principal component analysis (PCA) followed by multiple analysis of variance (MANOVA).https://www.cottongen.org/species/Gossypium_hirsutum/nbi-AD1_genome_v1.1).PCA extracted the dominant patterns in the trait matrix in terms of a complementary set of scores and loading plots , by replFor the second dataset, we also performed PLSR but not MANOVA. MANOVA generally requires further discriminant analyses or univariate comparisons, which are still under preparation by . To estipls and pls depot packages [All statistical analyses were performed using R statistical software version 3.2.4. , mainly packages .In the first dataset, we performed PLSR, PCA and MANOVA to detect associations between markers and the canopy traits CT, NDVI, CHT, and LAI.Through PLSR it was possible to detect correlations within markers, within traits, and between markers and traits as demonstrated by the biplot . The bip1, t2, t3. For instance, in t1 the coefficients were −0.72 for LAI, −0.61 for NDVI, and −0,63 for CT. A positive correlation was detected for CHT with a respective coefficient of 0.56 . Statistical significance was also difficult to find just based on the regression coefficients obtained from the PLSR. An efficient multivariate method to detect association is a MANOVA.To reduce the dimensionality of this complex dataset without the use of an index, we first needed to extract the principal components (PC) of the trait measurements. The first few principal components captured the major data variation and were then used for the MANOVA .After performing MANOVA, we detected 22 markers that were significantly associated (p<0.01) with drought resistance/tolerance in plants based on the Pillai-Bartlett Trace test  Figure .Significant markers were then annotated from the previously reported cotton dataset . SuccessThe second dataset contained the same 841 markers used in the first set of analyses. However, instead of looking at four drought related traits, we have 14 elemental traits P, K, Ca, Mn, Fe, Zn, Ni, Cu, As, Co, Rb, Mo, S, and Mg. For these analyses, we performed PLSR followed by jackknife.The biplot originated from the PLSR was very informative, showing that some traits were more correlated than others .For instance, latent vectors for Ni and Zn shows a high correlation as they are very close in the graph. In the same area, there is Fe, Cu, and Ca that can be said to have correlation with Ni and Zn. Another correlated set includes Rb, Mo, S and P. Mg is standing alone in opposition to Zn. In addition, the following ions also stand alone: Co, K, and As.Partial correlation coefficients within the traits were then extracted . ConsideIn order to detect statistical significance for the marker effect on the trait we performedjackknife resampling. Then, we were able to list the most singificant markers for P, K, Ca, Mn, Mo, and Rb . The resIn this work, we proposed the use of multivariate approaches to detect marker-trait associations in two cotton databases. For both, PLSR was effective as an exploratory method, especially to display correlation within traits.We have also observed that from the drought-related traits LAI, NDVI, and CHT are highly correlated. This finding suggests that LAI, NDVI and CHT can be combined in analyses as reliable drought indicators. CT was inversely correlated to the other three traits in our study. Even though we did not find correlation between CT and the other drought-related traits, there is evidence that CT relates to yield reductions associated with high temperature events .Pearson’s pair wise correlation coefficients tables are standard in plant research reports. Such tables can have massive information. Our PLSR bi plot can aid researchers to explore all their data, and visualize correlations in a more informative way.Conducting a MANOVA in addition to the PLSR, enabled the identification of 22 important markers for candidate drought related genes. After annotation, some important markers were found to be related to the 5- ubiquinol-cytochrome C reductase hinge protein, topless-related protein, tesmin/TSO1-like CXC domain-containing protein, DDB1-binding WD40 protein hypersensitive to ABA 1, NAC domain-containing protein, and the ABA receptor PYL8 OS.Ubiquinol-cytochrome C reductase hinge protein is involved in mitochondrial electron transport and it is in the mitochondrial respiratory chain complex III . The topMarker annotation was important to elucidate how drought is affecting plant development as well as to find lines that might have some tolerance to this a biotic stress. The annotation also confirmed that our analyses were useful, as they could detect markers associated with the drought-related traits. An example is the ABA markers DDB1-binding WD40 protein hypersensitive to ABA 1 and the ABA receptor PYL8 OS. The degree of biosynthesis and accumulation of ABA in a crop cultivar is a possible indicator of drought tolerance . In addiFrom the significant marker detected in this work, SNP013222 (a neurochondrin family protein) on linkage group 22, and MUSB1117a  on linkage group 45 were also detected by a univariate quantitative trait local (QTL) inclusive composite interval mapping (ICIM) approach performed by .For the second dataset with 14 elemental traits  we also conducted PLSR. The biplot with correlation among traits was very informative, showing highly correlated traits, inversely correlated traits and traits that were independent of the others.PLSR correlation coefficients within traits, within markers, and between markers and traits could be extracted from the analysis to give estimates of the marker effect on each trait.However, as mentioned previously, to find significant marker-trait associations, we applied a jackknife resampling technique. The newest updates on the pls R package became available on December of 2016 and included a jackknife option to perform approximate t-tests of regression coefficients based on jackknife variance estimates. In the literature, bootstrapping is also cited as an applicable resampling technique.The resulting p-values after performing jackknife should not be used uncritically, and should perhaps be regarded as mere indicator of (non) significance. This to the fact that the distribution of the regression coefficient estimates and the jackknife variance estimates are unknown (at least in PLSR/PCR) .PLSR is a very informative way to help comprehend how data are structured, displaying correlations within markers, within traits, and between marker and traits in one biplot.For the first dataset, PCA followed by MANOVA seemed to be an effective approach to detect association. However, further discriminant analyses might be needed if univariate analyses are not available. Furthermore, our first dataset univariate analyses were published by .PLSR offers partial correlation coefficients and resampling techniques are necessary to estimate variances. In this work, we used jackknife resampling but it failed to detect significant marker effects for several traits. This fact could also be due to no real effects of markers on the studied traits.Future work will include performing PLSR in other crops as well as looking at bootstrap as an alternative resampling technique. Overall, multivariate approaches in marker-trait association studies still need to be improved and broadly tested to leverage detection of additional variance and prevent spurious results.


When individuals interact, their phenotypes may be affected not only by their own genes but also by genes in their social partners. This phenomenon is known as Indirect Genetic Effects (IGEs). In aquaculture species and some plants, however, competition not only affects trait levels of individuals, but also inflates variability of trait values among individuals. In the field of quantitative genetics, the variability of trait values has been studied as a quantitative trait in itself, and is often referred to as inherited variability. Such studies, however, consider only the genetic effect of the focal individual on trait variability and do not make a connection to competition. Although the observed phenotypic relationship between competition and variability suggests an underlying genetic relationship, the current quantitative genetic models of IGE and inherited variability do not allow for such a relationship. The lack of quantitative genetic models that connect IGEs to inherited variability limits our understanding of the potential of variability to respond to selection, both in nature and agriculture. Models of trait levels, for example, show that IGEs may considerably change heritable variation in trait values. Currently, we lack the tools to investigate whether this result extends to variability of trait values. Here we present a model that integrates IGEs and inherited variability. In this model, the target phenotype, say growth rate, is a function of the genetic and environmental effects of the focal individual and of the difference in trait value between the social partner and the focal individual, multiplied by a regression coefficient. The regression coefficient is a genetic trait, which is a measure of cooperation; a negative value indicates competition, a positive value cooperation, and an increasing value due to selection indicates the evolution of cooperation. In contrast to the existing quantitative genetic models, our model allows for co-evolution of IGEs and variability, as the regression coefficient can respond to selection. Our simulations show that the model results in increased variability of body weight with increasing competition. When competition decreases, i.e., cooperation evolves, variability becomes significantly smaller. Hence, our model facilitates quantitative genetic studies on the relationship between IGEs and inherited variability. Moreover, our findings suggest that we may have been overlooking an entire level of genetic variation in variability, the one due to IGEs. Social interactions are common in nature, and other individuals are usually the most important part of the environment experienced by an individual Wolf . The envIn the traditional quantitative genetic model, the phenotype of an individual is the sum of the direct effect of its own genes (DGE) and an environmental effect. However, because the environmental effect includes a component due to the social environment, the phenotype of an individual is also a function of the genes of its social partners. The heritable effect of a social partner on the trait value of the focal individual is known as an Indirect Genetic Effect (IGE) Griffing . IGEs haIn the field of animal breeding, interest in social interactions has increased in recent decades, as both theoretical and empirical studies show that not only fitness but also trait values of individuals can be affected by genes of other individuals Muir , b. IGEsIn addition to the effects of social interactions on trait values, it has been observed in aquaculture populations that competition for feed and formation of social hierarchies also inflates trait variability Jobling . BecauseIndications of a close relationship between competition and variability are also coming from the field of plant breeding, where breeders have successfully improved productivity of crops by selecting, partly unintentionally, less competitive phenotypes, which also resulted in more uniform crops Donald . MoreoveThe variability of trait values of a genotype, measured either repeatedly on the same individual, or on multiple individuals belonging to the same family, has been studied as a quantitative trait in its own right. This trait is often referred to as “inherited variability” or “heritable variation in environmental variance”  chase and attack smaller conspecifics, but avoid larger individuals  breeding value for growth rate of individual i, Ep,GR,i and Et,GR,i are permanent and temporary non-heritable  effects of individual i, and bij is a regression coefficient.Therefore, we developed a basic quantitative genetic model involving interactions of two individuals. In this model, our target trait is growth rate between time point bij in our model measures the effect of a difference in body weight between the social partner and the focal individual on the growth rate of the focal individual. Hence, the absolute value of bij reflects the strength of the social interaction. When bij is negative, growth rate of individual i is reduced when j has higher body weight than i, indicating competition. Conversely, when bij is positive, growth rate of i is increased when j has higher body weight than i, indicating cooperation, i.e., “helping the one who lags behind” . The model described by Eq. The ind” Box . Thus, bψ is constant within a population , representing resistance to competition, and an indirect genetic effect of its social partner, representing cooperative effect . While b is a property of both the focal individual and its social partner, it affects the phenotype of the focal individual only; we will therefore refer to this b as “the b value of the focal individual”. Thus, for focal individual i with social partner j, the regression coefficient bij, i.e., the b value of the focal individual, is given byAD,i and ED,i are the direct genetic and environmental effect of individual i on bij, while AI,j and EI,j are the indirect genetic and environmental effect of individual j on bij. Appendix Trait-based IGE models usually assume that the “regression coefficient” tion Eq. . Howeverentclass1pt{minimab. In other words, our model shows that heritable effects on competition result in inherited variability. In the “Discussion” section, we further investigate how breeding values for b correlate with direct and indirect breeding values for inherited variability .Note that our model does not include an explicit breeding value for inherited variability. Instead, as shown in the section “Simulation” below, genetic variation in variability is an emerging property of the model, resulting from genetic effects of competition, i.e., the direct and indirect breeding values for We use the term “competition” to describe the situations where the larger individual continues to increase in size, while the smaller individual lags behind, leading to divergence of their body weights through time Fig. . This isime Fig. . This ocAD) and cooperativeness (AI), as these may be different properties of an individual. For example, consider the pair i and j in a population showing competition  and also resistant to competition , while j is very cooperative  but very sensitive to competition . Then the effect of j on i will be small, while the effect of i on j will be large , assuming Mendelian inheritance, while their environmental values were sampled from independent normal distributions. All individuals were randomly assigned to groups of 2 members. Phenotypes were constructed for 10 time points using Eqs. For each scenario, there were 100 replicates. Table The relationship between competition and variability generated by our model was assessed at two levels. First, we considered the average within-group variance of body weight at the last time point. Second, we considered the overall phenotypic variance in the entire population. Results are presented in Fig. 2  to 20.9 g2 , which is an 18-fold difference in variability of body weight between scenarios 1 and 5. The phenotypic variance ranged from 457.3 g2  to 95.1 g2 , showing a 5-fold difference in variability between scenarios 1 and 5. These results show that our model results in a relationship between competition  and V, demonstrate that the phenotypic variance within a group is directly related to the sum of b values within the group. The expressions show that the expected difference is zero if there is no initial difference at T = 0, while the variance depends directly on the sum of bij and bji. More details can be found in Appendix Expressions Appendix ppendix AAD) for b, as these individuals should be more resistant to competition. This links our model to the definition of inherited variability, where parents with low breeding values for variability have offspring with lower phenotypic variance. Figure AD of sires for b and variability of body weight of their offspring is negative, ranging from −0.55  to −0.20  across scenarios. This suggests that individuals that are genetically more resistant to competition are less variable. Moreover, offspring of sires with positive indirect breeding values (AI) for b should be less competitive. The group mates of these “social” individuals should therefore show less variability compared to group mates of individuals with negative indirect breeding values for b. In other words, AI of a sire affects the variability of phenotypes of the group mates of his offspring. As expected, Fig. AI of sires and variability of the group mates of their offspring. Figure AI of a sire and variability of his offspring, and between AD of a sire and variability of the group mates of its offspring. This result suggests a second-order effect; for the direct effect, for example, the AD of a sire first affects the trait values of its own offspring, which subsequently affects the variability of their groups mates in the next time period. For standard errors of the correlations see Supplementary file If a connection between competition and variability exists not only on the phenotypic level but also on genetic level, we should see less variation in body size among the offspring of sires that have positive direct breeding values  and indirect genetic effects (AI) for b with existing selection methods, we performed three types of selection: individual selection for body weight, group selection for body weight, and group selection for lower variance of body weight. In all three cases, selection was done using observations from time point 10. With individual selection, the 11 % of the heaviest individuals were selected as parents of the next generation. With group selection for body weight, the individuals from the 11 % of groups with the highest average body weight were selected. With group selection for lower variance, the individuals from the 11 % of groups with the lowest variance in body weight were selected. We illustrate the effect of selection by using base population with AD and AI, AD and AGR, and AI and AGR, were all set to 0. See Appendix To see how variability responds to selection, and whether we can capture direct .Our b for all groups, using the modelFirst, to estimate the overall average level of competition, one could fit single fixed b  additive genetic effects on growth rate. The b, where aD is a vector of random direct genetic effects on b, and Pt−1,j−Pt−1,i in the row and column for focal individual i. The b, where aI is a vector of random indirect genetic effects on b, and Pt−1,j−Pt−1,i in the row for the focal individual i and column for its group mate j. Hence, direct and indirect effects on b are so-called random regressions. Note that the above expression merely serves as starting point, and will have to be extended with non-genetic random effects, such random group effects and permanent individual effects variances of growth and the direct and indirect effects on entclass1pt{minimab of the sire. Figure b of the sire. Therefore, it may be possible to capture direct and indirect effects on b by fitting linear mixed models to the within-family variance, and to the variance of the group mates of a family, with sire as random effect. This analysis requires an appropriate family and group structure, but not time series data. More research is needed to see how breeding values for inherited variability correlate with direct and indirect effects on b, and how those effects can be fully captured.When time series data are not available, which may often be the case, another approach could offer a solution. Quantitative genetic models for inherited variability can be used to estimate genetic variance in variability from records on within-family variance. Figure b available in the literature. However, some indications for variation in b may come from estimates of ψ (psi) in so-called trait-based models of IGE  strain was paired with three individuals from a different, unrelated strain i.e. social strain. In that way, each focal genotype was tested against different social environments. The results of the study show that the level of Phenotypic uniformity is an important trait in animal breeding. In the pig industry, for example, it is desirable to deliver animals within a preferred range to the slaughter house, while deliveries outside that range result in penalties for the farmer Hennessy . In aquab.There is substantial evidence of a genetic basis of variability, which has been obtained through selection experiments and by quantifying genetic variation in variability  has a genetic component and is under stabilizing selection. In that study, phenotypic variability was considered either a trait of the individual, or a trait of its parents, and it was discussed how this view would change the interpretation of the genetic parameters. Here we focused at connecting differences in phenotypic variability between individuals to the level of competition, which may be useful for future studies on variability in natural populations.Mulder et al.  showed tKin-selection theory predicts that individuals should interact differentially with kin vs. non-kin, because this increases their inclusive fitness Hamilton . Togetheb from our model can respond to selection, and changes in b resulted in changes in variability, indicating the co-evolution of social interactions and inherited variability. Selection results showed that the effect of IGEs on b is ignored in classical mass selection, but can be partly captured by group selection on the mean or the variance. The latter also resulted in a decrease of variability. These findings suggest that we may have been overlooking an entire level of genetic variation in variability, the one due to IGEs. Genetic improvement of social effects, therefore, may be a promising route to reduce variability.We presented a quantitative genetic model in which direct and indirect genetic effects lead to inherited variability of trait values on the phenotypic level. The The data are available from the Dryad Digital Repository: 10.5061/dryad.c3k48j0bBox 1: Direct and indirect breeding values for AD) is the additive genetic effect of the focal individual on its own b and is referred to as a “resistance to competition”. Negative AD would mean that the individual is sensitive to competition, while the individual with positive AD is resistant to competition.Direct breeding value (AI) refers to additive genetic effect of a social partner on b of a focal individual. It is also referred to as “cooperativeness”. The social partner with negative AI is competitive, while the one with positive AI is cooperative.Indirect breeding value  = 2bij, and similarly ΔPt,j = bji = −2bij  is 0.02 g, while ΔPt,j = −0.02 g. However, if both individuals are competitive and sensitive to competition, AD,i = AD,j = AI,j = AI,i = −0.03, then ΔPt,i = −0.22 g, while ΔPt,j = 0.22 g. Hence, in a competitive environment, when both b are negative, the larger individual grows fast, while the growth of smaller one is slowed down. Positive breeding values in a competitive environment lead to small increase in growth for the smaller individual, and a small decrease for the larger one.In the competitive environment, where, for example, For explanation on chosen values see “Simulation and Appendix Cooperative environmentPt,i = 0.22 g, while ΔPt,j = −0.22 g. If both individuals have all negative breeding values of −0.03, then ΔPt,i = −0.02 g, while ΔPt,j = 0.02 g. Therefore, when both b are positive, the growth of the larger individual slows down, allowing the smaller individual to catch up. Negative breeding values in a cooperative environment lead to small increase in growth for the larger individual, and a small decrease in growth for the smaller individual.In the cooperative environment, where b, see Supplementary File For more scenarios and effects of combining positive and negative breeding values for Supplementary file 1(DOCX 17 kb)Supplementary file 2(XLSX 29 kb)Supplementary file 3(DOCX 1155 kb)Supplementary file 4(DOCX 16 kb)Supplementary file 5(DOCX 13 kb)Supplementary file 6(DOCX 20 kb)


TPH1 A779C polymorphism and maternal parenting styles on creative potential. The results showed that there was a significant interaction of TPH1 A779C polymorphism and maternal authoritarianism on creative potential. Moreover, the analysis of regions of significance (Ros) provided supporting evidences for both the diathesis-stress model (flexibility) and the differential susceptibility model . These findings extend our understanding concerning the mechanisms by which gene and environment may act in coordination to contribute to creativity.Exploring the possible mechanisms through which gene may interact with environment to influence creativity has been one of the leading issues in creativity research. In a sample of four hundred and twenty-one Chinese undergraduate students, the present study investigated for the first time the interaction of  TPH1). TPH1 is located on chromosome 11, and is expressed in both human central and peripheral nervous system , but yielded inconsistent results  of creative potential, and demonstrated that TPH1 A779C polymorphism was only associated with fluency. By including both tag single nucleotide polymorphisms (SNPs) and functional SNPs, TPH1 and creative potential, but found that TPH1 A779C polymorphism was not related to any of the three core dimensions of creative potential.Previous studies examining the association of  results . Reuter As for these inconsistent results, there are a number of possible reasons . However, since creativity, like most of other complex traits, is determined by the interplay of gene and environment, it is reasonable to suspect that the primary reason that accounts for the discrepancy may be attributed to the neglect of gene–environment (G × E) interaction .TPH1 A779C polymorphism to influence creative potential is maternal parenting styles. Parenting styles represent the emotional connections and the quality of contacts parents make with their children, and it has been shown that maternal parenting styles are critical environmental factors for individual’s creativity (DRD2 genotype (rs1799732) could interact with maternal parenting styles to affect creative potential . The present study was approved by the Institutional Review Board of Shandong Normal University. Written informed consent was obtained from each participant.Creative potential was assessed by three Uses tasks selected from Runco’s Creativity Assessment Battery (rCAB). The Uses tasks asked the participants to list as many as possible uses for three common subjects , and were comparable to other assessments of creative potential . For eacMaternal parenting styles were self-reported by participants using the Parental Authority Questionnaire (PAQ) which was developed to measure the authoritative, authoritarian and permissive parental authority prototypes proposed by TPH1 A779C polymorphism were performed at Beijing Genomics Institute-Shenzhen by using the Sequenom MassARRAY iPLEX system according to the manufacturer’s instructions. For quality control, 5% random DNA samples were genotyped twice to calculate genotyping error. The genotyping accuracy was 100%.Peripheral venous blood samples from each participant were first collected with the assistance of medical staff. Genomic DNA was extracted from peripheral venous blood samples by using the Qiagen QIAamp DNA Mini Kit. Genotyping for TPH1 A779C polymorphism and maternal parenting styles on creative potential, hierarchical multiple linear regression was conducted by using SPSS version 24.0. The procedure was as follows: covariates (gender) were entered in the first step to control for the confounding effects. The main effect of TPH1 A779C polymorphism (dummy-coded as 0 = CC versus 1 = AA/AC) and maternal parenting styles were entered in the second step. Finally, the interaction terms for TPH1 A779C polymorphism and maternal parenting styles were added in the third step. When significant interaction was found, simple slope analysis was conducted by using the PROCESS macro for SPSS version 2.16  represents the upper and lower bounds of values for the predictor (X) at which the regression of the outcome (Y) on the moderator (Z) is statistically significant. If the association between the moderator (Z) and the outcome (Y) is significant at both the upper and lower ends of the predictor (X) within +/−2 SD, then the differential susceptibility model is supported. Second, the proportion of interaction index (PoI) measures the proportion of the total interaction that is represented on the right side or the left side of the crossover point for the interaction, indicating how much a crossover interaction is “for better” or “for worse.” PoI values between around 0.40 and 0.60 indicate an interaction highly consistent with the differential susceptibility model, while PoI values close to 0 or 1 suggest strong supporting evidence for the diathesis–stress model. Third, the proportion affected index (PA) estimates the proportion of the population that is differentially affected by the moderator (Z). PA values around 0.50 indicate strong evidence for the differential susceptibility model, while PA values close to 0 or 1 provide strong evidence for the diathesis-stress model. Finally, the test of non-linear effects ascertains whether the apparent differential susceptibility effect could be artifacts of imposing a linear model on a non-linear diathesis-stress phenomenon. To support the differential susceptibility effect, the results of the model must show that the linear interaction term remains significant after controlling for the non-linear terms (quadratic effects: X2 and ZX2).To test whether the significant G × E interaction supported the diathesis-stress or the differential susceptibility model, the analysis of regions of significance (RoS) recommended by TPH1 A779C polymorphism genotypes were CC , AC , and AA , respectively. No deviation from Hardy-Weinberg equilibrium was observed (p = 0.49). Table TPH1 A779C polymorphism nor other maternal parenting styles was correlated with the three scores of creative potential.The number of participants as well as the frequencies for TPH1 A779C polymorphism × maternal authoritarianism interactions on flexibility and originality , but not for those with the AA/AC genotype ; maternal authoritarianism negatively predicted originality for individuals with the CC genotype , but not for those with the AA/AC genotype  , whereas over 80% was right of the crossover point (“for worse”). The PA indexes indicated that 24% of individuals were affected “for better” , while 76% were affected “for worse.”For flexibility, the analysis of RoS provided supporting evidence for the diathesis-stress model Figure . The RoSX test revealed that the regression of originality on TPH1 A779C polymorphism was significant at both the upper and lower bound of maternal authoritarianism within +/−2 SD of the mean. Both the PoI and the PA indexes were close to 0.50. Test of non-linearity revealed significant quadratic effects of X2 . However, when controlling for the non-linear term by adding it to the original model, the interaction of TPH1 A779C polymorphism and maternal authoritarianism remained statistically significant.For originality, the analysis of RoS demonstrated supporting evidence for the differential susceptibility model Figure . The RoSTPH1 A779C polymorphism and parenting styles on creative potential has both produced mixed results; however, the exact reason concerning the discrepancies has not yet been identified. By revealing the interaction of TPH1 A779C polymorphism and maternal parenting styles on creative potential, the present study suggested that the neglect of potential G × E interaction might be one of the primary reasons that account for the discrepancies.Previous research focused on the effect of TPH1 A779C polymorphism and maternal authoritarianism was found on creative potential. It was shown that the negative effect of maternal authoritarianism on creative potential was only present for individuals with the CC genotype, but not for those with the AA/AC genotype, suggesting that the CC genotype might be more sensitive to high maternal authoritarianism.In the present study, significant interaction of TPH1 encodes the rate-limiting enzyme for serotonin biosynthesis in the neurons of the raphe nuclei  but lower originality than those of the AA/AC genotype when there was high maternal authoritarianism . These findings suggested that the potential mechanisms underlying the G × E interaction on creativity might be complicated. For different dimensions of creativity, there might be different G × E interaction patterns, and genes could be either “risk” or “plasticity” to modulate the effect of environment on creativity.To clarify the G × E interaction pattern for the significant interaction of TPH1 A779C polymorphism to influence creative potential. This result was coincided with previous finding that, among the three different parenting styles, only authoritarian parenting interacted with DRD2 to affect creative potential (TPH1 A779C polymorphism), to maximize their creative potential, avoiding the effect of adverse environment  might be at least as important as, or even more important than proactively creating positive environment .Moreover, although three different maternal parenting styles were tested in the present study, only maternal authoritarianism was found to be interacted with otential . These eTPH1 A779C polymorphism and maternal authoritarianism on creative potential. However, since intelligence was not measured in the present study, this hypothesis could not be examined. Future studies are warranted to test this hypothesis. And it has also to be elucidated whether the effect of serotonin is directly exerted or by an indirectly interaction with the dopamine system, since it has been shown that serotonin can inhibit dopamine activation (TPH1 A779C polymorphism) was examined in the present study, the full contribution of gene and parenting styles interaction to creativity was far more from being revealed. For future studies aimed to fully uncover the interaction of gene and parenting styles on creativity, polygenic score derived from GWAS of creativity may be an ideal candidate genetic index to test the interaction of genes and parenting styles. And there has been one successful attempt using GWAS data to explore both the neural and genetic determinants of creativity  of maternal parenting styles are guaranteed to provide more comprehensive and convincing results. Third, although the present study provides plausible explanation for the significant interactions, the exact mechanisms underlying these interactions remains to be clarified and refined. Because serotonin is involved in multiple emotional, cognitive and behavioral control process and the modulation of serotonin transmission is a complex network of different biological process , sortingtivation . Moreovetivation . As for eativity .TPH1 A779C polymorphism and maternal authoritarianism on creative potential. These findings may provide important insight into how gene interacts with environment to influence creativity, and help to explain the origins of individual differences in creativity.In conclusion, the present study shows the first evidence for the interaction of SZ and JZ were involved in the conception and design of the work. SZ, XH, and SS collected the data. SZ analyzed the data and contributed in writing the main manuscript text.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.


The intrauterine environment is critical for fetal growth and development. However, observational associations between maternal gestational lipid concentrations and offspring birth weight (BW) have been inconsistent and ascertaining causality is challenging.n = 188 577 European-ancestry individuals; sample 1) were selected as instrumental variables. The effects of these SNPs on offspring BW were estimated using a structural equation model in the UK Biobank and Early Growth Genetics consortium  that enabled partitioning of the genetic associations into maternal- (intrauterine) and fetal-specific effects.We used a novel two-sample Mendelian randomization (MR) approach to estimate the causal effect of maternal gestational high-density lipoprotein cholesterol (HDL-C), low-density lipoprotein cholesterol (LDL-C) and triglyceride concentrations on offspring BW. Single nucleotide polymorphisms (SNPs) associated with serum HDL-C, LDL-C and triglyceride concentrations identified in the Global Lipids Genetics Consortium genome-wide association study meta-analysis , LDL-C = 0.014 , and triglycerides = 0.014 ].Our findings suggest that maternal gestational HDL-C, LDL-C and triglyceride concentrations play a limited role in determining offspring BW. However, we cannot comment on the impact of these and other lipid fractions on fetal development more generally. Our study illustrates the power and flexibility of two-sample MR in assessing the causal effect of maternal environmental exposures on offspring outcomes. We used a novel two-sample Mendelian randomization design to investigate the causal effect of maternal gestational lipid concentrations on offspring birth weight.We used summary statistics from genome-wide association studies that predict serum high-density lipoprotein cholesterol, low-density lipoprotein cholesterol, and triglyceride concentrations and birth weight, with the latter being partitioned into maternal- and fetal-specific effects.Our findings showed limited support for a causal effect of maternal gestational high-density lipoprotein cholesterol, low-density lipoprotein cholesterol, and triglyceride concentrations on offspring birth weight.The same method could be used to examine other maternal exposures putatively causally related to offspring outcomes assessed later in life. On average, babies born at term below the 25th percentile or above the 85th percentile of the population distribution for birth weight (BW) in high-income countries are at higher risk of adverse perinatal outcomes, such as stillbirth, neonatal mortality, respiratory problems and the need for admission to neonatal intensive care.,,2 2).,Maternal serum lipid concentrations are one such trait that could influence offspring BW. Observational studies have reported inconsistent results regarding the relationship between maternal lipid concentrations and offspring BW. For example, maternal serum high-density lipoprotein cholesterol (HDL-C) concentrations have been reported to have positive,Mendelian randomization (MR) is a method commonly used in epidemiology to estimate the causal relationship between a modifiable environmental exposure of interest and a medically relevant trait or disease.,n = 9176].Unlike MR studies investigating the causal relationship between two adult traits, estimating the causal effect of maternal exposures on offspring outcomes using MR is difficult due to the fact that maternal  genotype determine offspring genotype. Specifically, any association between maternal genotype and offspring outcome could be mediated by the child’s genotype rather than through the maternal genotype operating on the intrauterine environment . To ensuAn alternative solution, which we adopt, is to employ two-sample MR to estimate the causal effect of maternal lipid concentrations on offspring BW, but using unbiased estimates of the maternal genetic effect on BW from a very large GWAS meta-analysis of the UK Biobank and the Early Growth Genetics (EGG) Consortium.In a recent study using this novel two-sample MR approach, we demonstrated a positive causal effect of maternal height and fasting glucose and inverse causal effect of blood pressure on offspring BW,n = 188 577 European-ancestry individuals; sample 1)n = 230 069 European-ancestry individuals; sample 2).To investigate the causal relationship between maternal lipid concentrations and offspring BW we initially performed two-sample inverse variance weighted (IVW) MR analysesP < 5.0 x 10–8) and were selected as instrumental variables (IVs) for MR analyses (IJE online). Of these SNPs, 96 were associated with HDL-C, 82 were associated with LDL-C, and 60 were associated with triglycerides, all at the genome-wide significance level of P < 5.0 x 10–8. We refer to these SNPs as the ‘Unrestricted Set’ of SNPs for each of the three serum lipids. As many of these SNPs were associated with more than one lipid fraction, which potentially violates the exclusion restriction assumption of IVW MR analysis, we created a ‘Restricted Set’ of SNPs, which had strong evidence of association with one lipid fraction only (i.e. P < 5.0 x 10–8 for one lipid and P > 0.05 for the other two). This reduced the number of associated SNPs to 15 SNPs for HDL-C, 20 SNPs for LDL-C, and 3 SNPs for triglycerides (IJE online). We did not perform MR analyses using the ‘Restricted Set’ for triglycerides because the 3 SNPs together only accounted for <0.1% of the phenotypic variance in serum triglyceride concentrations and calculations indicated low power to detect a causal relationship of maternal triglycerides on BW.The exposure variables of interest were maternal concentrations of three serum lipid fractions: HDL-C, LDL-C and triglycerides. A total of 185 independent SNPs have previously been robustly associated with these three lipid fractions , we performed four sensitivity analyses using additional MR models, MR Egger regression,GX statistic is a value ranging between 0 and 1, with the value close to 1 indicating that the SNP-exposure associations are sufficiently heterogeneous and the uncertainty is relatively small compared with its variability so the violation of NOME is negligible.MR Egger regression involves a weighted linear regression of The weighted median estimator approach uses the weighted median of the ratios , which make different assumptions regarding instrument validity, produce similar estimates of the causal effect, then we can be more confident in the robustness of our findings.P < 0.05 and 5.0 x 10–8, respectively; IJE online).Two multivariable MR analyses, multivariable IVW regressionThe multivariable IVW regression was performed by regressing The multivariable MR Egger regression was performed also by including all 185 lipid-associated SNPs  and there was a lack of asymmetry of the funnel plots (IJE online). We also found little evidence for violation of the ‘NOME assumption’ for the MR Egger regression as the IGX statistics were >97.5% for all analyses .There was little evidence for a causal effect of maternal gestational concentrations of HDL-C, LDL-C or triglycerides on offspring BW . Each esThe two-sample MR IVW analysis showed no causal effect of maternal HDL-C level and offspring weight [SD change in BW per 1SD higher in HDL-C = −0.005 ]. This was supported by all univariate and multivariable sensitivity analyses  and 4A, IJE online). However, this estimated positive causal effect was not supported by all other univariate and multivariable analyses. The SNP rs1998013 appears to be an outlier in the scatterplot (IJE online).While no causal effect was found in the univariate IVW analysis [SD change in BW per 1SD higher in LDL-C = 0.014 ], a higher genetically predicted level of maternal LDL-C tended to be associated with a higher offspring BW in the weighted median [SD change in BW per 1SD higher in LDL-C = 0.109 ] and weighted mode-based [SD change in BW per 1SD higher in LDL-C = 0.118 ] analyses using the ‘Restricted Set’ of SNPs ], which was supported by the sensitivity analyses  and 4C.We employed a novel methodological approach to assess the causal effect of maternal concentrations of LDL-C, HDL-C and triglycerides on offspring BW using a two-sample MR framework. The major difference between our approach and standard two-sample MR is that the SNP-outcome associations (i.e. SNP-BW associations) have been partitioned into maternal and fetal genetic components, which has allowed us to estimate the effect of maternal exposures on BW, independent of the fetal genetic effects. We applied this method to examine the causal effect of maternal gestational LDL-C, HDL-C and triglycerides on offspring BW, while controlling for fetal genotype, and found little support for a causal effect of these on offspring BW.Results from this study are consistent with our previous MR study using a smaller sample of genotyped mother–offspring pairs for HDL-C although we do not find any evidence of a suggested inverse effect of triglycerides on birthweight reported in that previous study.,We emphasize that the null associations we found do not necessarily mean that maternal LDL-C, HDL-C and triglyceride concentrations have no effect on the developing fetus. They suggest that these maternal circulating lipid fraction concentrations have no effect on the overall growth of the fetus that is reflected by BW. Maternal circulating LDL-C, HDL-C and triglycerides could still impact the development of a particular organ, growth during a particular period of pregnancy, or differential growth of fat, lean and skeletal tissue, but we could not detect these effects by looking only at BW. Several small detailed studies have documented how maternal lipid and fatty acid concentrations change across pregnancy, showing particularly marked increases in triglycerides and more modest increases in cholesterols and phospholipid concentrations together with an increase in the proportion of triglycerides carried in very low-density and low-density lipoprotein particles towards the end of pregnancy.,et al.).A key assumption of our study design is that SNPs associated with lipid concentrations in the general population of men and (non-pregnant) women are appropriate instruments for lipid concentrations in mothers during pregnancy. Our concern arises from the fact that maternal lipid concentrations change dramatically during pregnancy,,Another potential complication in interpreting the results of these sorts of MR analyses is the extent to which one can be sure that the causal estimates reflect the effect of the prenatal environment on the developing offspring. For example, it is possible that variation in circulating lipid concentrations before conception might affect oocyte quality and then have downstream effects on offspring BW.There are no obvious technical reasons why our method cannot be applied more generally to outcomes other than BW. The major practical limitation, however, is the availability of large-scale cohorts with maternal genotypes along with both maternal and offspring phenotypes so that unbiased estimates of maternal genetic effects on offspring outcomes can be made available to researchers for two-sample MR studies. One way to directly facilitate the availability of these kinds of data to the scientific community would be for researchers to publish summary GWAS results of maternal genotype and offspring phenotype, conditional on offspring genotype. However, performing conditional association analyses across the genome is computationally intensive, and may be difficult for many researchers to implement. A more practical alternative might be for investigators to deposit unconditional GWAS results of the association between maternal genotype and offspring phenotype and separate unconditional GWAS results between offspring genotype and offspring phenotype. These summary results could then be used in a structural equation model to generate unbiased estimates of maternal and fetal genetic effects on offspring phenotype, even when the degree of sample overlap is unknown.Maternal gestational LDL-C, HDL-C and triglyceride concentrations do not appear to play a causal role in determining offspring BW. Our study illustrates how causal estimates of maternal environmental exposures on offspring BW can be generated in extremely large samples of individuals using a two-sample MR framework, obviating the requirement for mother–offspring duos with individual level genotypes. The implication is that the same method could be used to examine other maternal exposures putatively causally related to offspring BW, and potentially the relationship between maternal exposures and other offspring outcomes once large scale GWAS of maternal effects are publicly available.D.M.E. is supported by an NHMRC Senior Research Fellowship (GNT1137714) and this work was supported by a project grant (GNT1125200). D.A.L’s contribution to this piece is supported by the European Research Council under the European Union's Seventh Framework Programme (FP/2007–2013) / ERC Grant Agreement , the European Union’s Horizon 2020 research and innovation programme under grant agreement No 733206 (LifeCycle), the United States National Institutes of Health (NIH): National Institute of Diabetes and Digestive and Kidney Diseases (R01 DK10324), and the British Heart Foundation (AA/18/7/34219). D.M.E and D.A.L work in a UK Medical Research Council (MRC) Unit that is supported by the University of Bristol and MRC (MC_UU_00011/6), and D.A.L. is a National Institute of Health Research Senior Investigator (NF-SI-0611–10196). N.M.W. is supported by an Australian National Health and Medical Research Council Early Career Fellowship (GNT1104818). R.M.F. is supported by Sir Henry Dale Fellowship . This research has been conducted using the UK Biobank Resource (Reference 12703). Access to the UKBB study data was funded by University of Queensland Early Career Researcher Grant (2014002959). L.-D.H is supported by a National Health and Medical Research Council project grant (GNT1125200). This research was carried out at the Translational Research Institute, Woolloongabba, QLD 4102, Australia. The Translational Research Institute is supported by a grant from the Australian Government. No funders influence the study design, data collection or interpretation of results. The views expressed in this paper are those of the authors and not necessarily any funder.Conflict of interest: D.A.L has received research support from several national and international Government and charity funders, and from Medtronic Ltd and Roche Diagnostics in the last 10-years. All other authors report no conflicts of interest.dyz160_Supplementary_DataClick here for additional data file.