The social sciences have been reticent to integrate a biodemographic approach to the study of fertility choice and behaviour, resulting in theories and findings that are largely socially-deterministic. The aim of this paper is to first reflect on reasons for this lack of integration, provide a review of previous examinations, take stock of what we have learned until now and propose future research frontiers. We review the early foundations of proximate determinants followed by behavioural genetic (family and twin) studies that isolated the extent of genetic influence on fertility traits. We then discuss research that considers gene and environment interaction and the importance of cohort and country-specific estimates, followed by multivariate models that explore motivational precursors to fertility and education. The next section on molecular genetics reviews fertility-related candidate gene studies and their shortcomings and on-going work on genome wide association studies. Work in evolutionary anthropology and biology is then briefly examined, focusing on evidence for natural selection. Biological and genetic factors are relevant in explaining and predicting fertility traits, with socio-environmental factors and their interaction still key in understanding outcomes. Studying the interplay between genes and the environment, new data sources and integration of new methods will be central to understanding and predicting future fertility trends. Fertility research within demography and the social sciences has been largely dominated by social science or environmental explanations of fertility behaviour and outcomes  and take an effort to describe methods that are less familiar to social scientists  in the text and accompanying Appendices.We have opted to organize our scientific history of the biodemography of fertility around several themes. We first review the main reasons for the lack of attention—and in some cases outright resistance—to adopting a biodemographic approach to fertility research. We then discuss the early foundations of combining a biological and behavioural approach to the study of fertility via the use of proximate determinants. Next, we turn to a review of research that has adopted a behavioural genetic approach to determine whether fertility has a genetic component, often using family and twin study designs. This is followed by more recent research in the area of molecular genetics, which shifts from identifying whether there is a genetic component to fertility to isolating where it is located. Anthropological and evolutionary approaches are then touched upon. The paper concludes with a broader discussion that reflects upon what we have learned until now and potential future fertile frontiers in this area of research. Finally, Appendices and Footnotes provide more detailed explanations of the central terms used in this paper which may be unfamiliar to a social science audience.tempo (or timing) of childbearing and the quantum or actual number of children that women have during a certain period. Throughout this study, we also often refer to two of the most central indicators studied in this field until now, which is the tempo measure of age at first birth (AFB) and the quantum measure of number of children ever born (NEB).Before embarking upon this review, it is useful to first define the terminology related to ‘fertility’ as it often differs across disciplines. Throughout this paper we generally refer to human fertility and not cross-species research. It is also essential to note that the broader terms fertility and infertility have different meanings in demography, evolutionary biology and reproductive medicine .This reluctance, lack of data and interdisciplinary training that combines strong social and biological or genetic measures has resulted in fertility theories and explanations in the social sciences that are generally socially deterministic, often solely based on explanations related to agency, motivation, conscious choice and intentions , and is defined as the fraction of the overall variance of a trait in a population that is caused by (additive) genetic effectsThe statistical concept used to measure genetic influences on a trait within a population is called Traditional family-studies follow simple designs such as parent-offspring correlations. Parents and children share on average 50 % of their genes. This entails two times the observed correlations in a trait. For example, the number of children ever born (NEB) estimates the heritability assuming that the shared environment of family members does not play a role in the correlation of the NEB. Correlations in fertility are very common among family members and also increased during the Twentieth century Murphy . It shouThe pioneering work of Fisher  found anThe most common way to disentangle influences of latent family factors on any trait of interest is to use the information available in twin data. Twin models follow a relatively simple and straightforward logic and until now, represent one of the best resources for evaluating the importance of genetic variation in observed traits  and fraternal dizygotic (DZ) twins, in order to quantify genetic and non-genetic environmental influences. In a classic twin design, MZ as well as DZ twins are siblings of virtually identical ages and born and raised in the same families. The siblings are consequently assumed to share common environmental influences such as their parents, the neighbourhood they grew up in and other related aspects. More importantly, MZ twins are genetically identical . DZ twins in contrast, are akin to full siblings and thus share on average only around 50 % of additive genetic effects. Similar to parent–offspring correlations, the correlation among DZ twins therefore reflects the importance of both environmental and genetic effects in families. The degree, however, to which MZ twins have a higher correlation in the trait of interest than DZ twins, reflects the fact that they are genetically more similar. The comparison of twin correlations thus already makes it possible to quantify genetic and shared environmental effects related to a particular trait (for details regarding the quantitative models to estimate these effects see Appendix 2) , age at first birth (AFB), which we summarize here.Several (twin) studies provide evidence for a genetic component underlying both the tempo (AFB) and quantum (NEB) of human fertility up to a level of over 40 %  has been assessed in a recent study by Nisén et al.  on FinniA core issue in the analysis of AFB is the handling of right-censored observations . Opposed to the commonplace practice of including right-censored cases in demography and sociology  interaction has also been examined in the study of NEB. Using data on the historical Danish twin cohorts including virtually every twin pair born since 1870, Kohler et al.  and KohlAs described in more detail previously, this fits with the explanation hypothesized by Udry  who descFollowing Udry’s  hypothesAttention to gene and environmental interactions have also been found in studies that focus on the AFB. A study by Tropf et al.  analysedAlthough the focus until now in this review has been on NEB and AFB, other related fertility traits have also been examined. Genetic influences have been explored for the age at first dating or marriage  modelling  or number of children (NEB) to date, several fertility-related studies have been conducted on sexual behaviour and contraceptive use. These studies examined the impact of certain pre-hypothesized genetic polymorphismsGuo and Tong  conduct Halpern et al.  examinedGuo et al.  examinedAnother study by Daw and Guo  drawing Although these results have been path-breaking, the candidate-gene approach has more recently been highly criticized (for a review see for example Ioannidis −8) in order to be considered as validated. A positive association refers to the case where there is a greater frequency of a genetic variant in individuals with that trait compared to those in the control group . The association identifies a genomic region and not a specific causative mutation that might be involved in the development of the trait or behaviour.After the backlash of candidate-gene studies, Genome Wide Association Studies (GWAS) emerged as a promising new approach to connect genetic variants to the outcomes of interest . At the time of writing this review, Mills and her research team at the University of Oxford are currently leading a large consortium to engage in the first ever genome-wide association search (GWAS) and meta-analysis of reproductive choice , conducted in both men and women in over 50 data sets, with the results replicated in additional datasets in a large sample.A promising first application in the social sciences examined the genetic variants to predict educational attainment on more than 120,000 genotyped individuals by Rietveld et al.  as part Although GWAS are able to narrow in on where to look in the genome, recent research has criticized . Previous research has successfully demonstrated that there is a genetic component to reproduction with over 70 genome-wide association studies (GWAS) published for 32 traits and diseases associated with reproduction found  than for traits such as fertility . Since it is highly implausible that even the best social scientist could specify the biological pathway and isolate particular genetic variants in advance, this approach offers an alternative. We then reviewed results of several studies in evolutionary anthropology and biology that showed that contemporary populations might still be under natural selection . Second, biological predispositions may affect the processes of decision-making and life course planning, consciously and subconsciously (Kohler et al. The growing interest and study of epigenetics is another relevant consideration for future research (Landecker and Panofsky Almost identical results in heritability estimates for men and women e.g. (Rodgers et al. Evolutionary predictions that there is a tendency to have children at a younger age over time seem to contradict widespread observations of fertility postponement at the population level in many European countries. Models from biologists suggest that the AFB decreases across generations (Byars et al. As mentioned at the onset of this review, a central reason for the lack of biodemographic research in the area of fertility has been a lack of data that combines good social science indicators with data that has biomarker and genetic data in large samples. The recent significant reduction in the costs of collecting, storing and processing this type of data will hopefully result in new sources for the future. Although considerable research has been done, many questions remain open. The fact that heritability is a population parameter and therefore can vary over time and space requires replication of heritability estimates in different societies of interest.To break new frontiers in fertility research using genetic information, methodological advances such as the ACE-β has been developed that bridge behavioural genetic and econometric approaches. This approach combines insights from econometrics and behavioural genetics by integrating the MZ-fixed effects approach as a direct link between phenotypes into the structural equation model. It therefore potentially identifies a causal link between two traits additional to genetic and environmental endowment—particularly if a valid instrumental variable can be found (these and related approaches are detailed in Kohler et al. Additional techniques have also been developed within quantitative genetics to try to explain more of the variance predicted in behavioural genetics models or in other words to address the ‘missing heritability’ problem. Several methods combine many SNPs to aggregate the collective effect and achieve a higher level of predictive power such as polygenic risk scores (Purcell et al. A central conclusion from this review is that biological and genetic factors are relevant in explaining and predicting fertility traits. The socio-environment, which demographers and social scientists have studied until now, however, still appears to account for the major part of the observed variance. Studying the interplay between genes and the environment, new data sources and integration of new methods will be central to more effectively understanding and predicting fertility trends. Findings, such as the common genetic base of the first attempt to have a child and NEB furthermore suggest that genes not only mediate physical but also psychological traits and conscious decision making. In the coming years we anticipate that the field and interest will grow as we become able to isolate which genetic variants are important for fertility, understand their biological functions and how they interact with the socio-environment.


The application of family-based tests to whole-genome sequenced data provides a new window on the role of rare variant alleles in the etiology of disease. By applying family-based tests to these data, we can now identify rare variants associated with disease. Approaches for common variants, by contrast, require large sample sizes for power, and are powerless when faced with rare variants. When we tested Yip et al's 2011 family-based association tests for rare variants on pedigrees from the Genetic Analysis Workshop 18, we found that weighted collapsing methods generally have more power than unweighted methods, but are more prone to type I errors. We then evaluated a sliding window modification of the weighted family-based association tests for rare variants method. Although this modification inflates the rate of false positives, it significantly increases the power of family-based association tests for rare variants to identify causal rare variants. Until next-generation sequencing (NGS) technology became widely available, genetic studies, including genome-wide association studies (GWAS), were generally based on the assumption that common diseases are driven by common variants (CD-CV). Although studies based on the CD-CV approach have had some success in identifying variants related to genetic disorders, their performance with regard to more complex diseases (such as hypertension or various psychiatric conditions) has been limited at best . ResearcBecause disease-related variants are likely to be both widespread in distribution and rare in frequency, GWAS data, which covers only a small portion of the genome, may not provide a representative sample in which to find them. By contrast, whole genome sequencing (WGS) technologies not only provide more complete coverage of the genome, but also of individual variants within genes. New ways to analyze and interpret WGS data are needed, however, because WGS is still costly, sample sizes are relatively small, and the disease-related variants are rare. Toward that end, family-based association test (FBAT) analyses, which enrich the occurrence of rare variants within pedigrees, provide a new approach to identify rare and possibly disease-related variants. This study shows how well the pedigree-based FBAT-rare method developed by Yip et al  performsIn this study, 2 FBAT-rare methods of statistical analysis were tested on the Genetic Analysis Workshop 18 (GAW18) data set based on the San Antonio Family Studies. GAW18 data includes 1389 individuals in 20 large pedigrees, with a maximum of 5 generations per pedigree. Subjects are randomly selected low-income Mexican Americans and their extended pedigree members. Study probands range in age, on average, between 40 and 60 years. The genotype data is cleared of mendelian errors on odd-numbered chromosomes, and comes from 959 individuals. Of these, 464 were sequenced at 60× coverage. Data from the rest were imputed. In total, the genotype data used in this study included 8,348,674 variants. For the purpose of assessing statistical methods, a set of genes were selected and their effect sizes calculated based on their correlation with hypertension, as well as their PolyPhen scores; 200 replicates of phenotypes were simulated. This set of genes is listed in the GAW18 answers. For convenience, we refer to the genes used to simulate phenotypes as true causal genes and the rest as noncausal. With this information, we assessed the power and false-positive rates of FBAT-rare, [In collapsing methods of statistical analysis, the effects of individual rare variants are combined linearly and the resulting sum is treated as a single variant. Many studies have been conducted to develop collapsing algorithms powerful enough to detect rare variants . FBAT-raζ is the total number of nuclear families and kth variant estimated from the sample. This weight scheme follows that used by Madsen and Browning [In this study, we investigated 2 different weighting schemes for test statistics implemented in the FBAT software (FBAT v2.0.4 beta 1). Under the FBAT-v0 test, the weights are defined as: 1, that is Browning  to estimp values for each gene. We observed that these p values often differ from each other by several orders of magnitude, preventing us from averaging all 200. Thus, we needed appropriate measures to compare different genes. To achieve this, we looked at a decreasing series of powers of 10. For an arbitrary gene, we calculated the fraction of p values that falls below 1*Both methods were tested for each gene on chromosome 3 and repeated 200 times for each replicate, resulting in 200 http://hgdownload.cse.ucsc.edu/goldenpath/hg19/database/). To highlight the statistical properties of rare variants, we selected variants with minor allele frequencies (MAFs) of <0.01, based on the founder population, for each gene. Using both v0 and v1 methods, we collapsed rare variants for each gene into a single variant. Both methods were then applied to all 200 replicates of simulated phenotype data, with the focus on the SBP_1 trait, which is the first systolic blood pressure measurement out of 4. Possible effects of sex, age, and medication on SBP_1 were taken into account to generate a corrected ASBP_1 phenotype, which was then analyzed in the same way as the uncorrected SBP_1 phenotype.This study focused solely on chromosome 3. We defined genes according to the hg19 database  was tested using true causal genes from chromosome 3 . Based on our results for all causal genes, it is clear that the v1 method consistently outperforms the v0 method and is more sensitive than v0 for the detection of causal variants. In our data, if the p value for v1 falls below 0.1, then the v1 test consistently performs better than v0 for all cases tested.Of the true causal genes, collapsed rare variants within To assess the validity of both methods, we selected all noncausal genes from chromosome 3  to calculate the probability of chance findings. See Figure p value of At the significance threshold MAP4 and SCAP were detected at the That of 31 true causal genes simulated on chromosome 3, only MAP4 as an example, the entire genetic region spans across 4 such windows. The reasoning is that any clustering of causal variants to fall within such a window will show up prominently. We then tested for rare variants using FBAT-v1 on data from each window, in the same manner as we tested the 2 FBAT methods on individual genes. MAP4 results .First, we divided the entire chromosome into a series of disjointed 100-kilobase (kb) windows with the whole 100kb points on the genetic positions  as the starting and ending points. Using MAP4, FBAT-v1 detected variants in the 47900 to 48000 kb and 48100 to 48200 kb windows with the same power as the gene-based method, and in the 48000 to 48100 kb window, detection even reached a power of MAP4 can achieve. With most causal genes, results from FBAT-rare v1 analysis of the best window are an order of magnitude better than the results from gene-based analysis. The sliding-window approach, however, tends to result in more false positives (data not shown).For windows completely contained within MAP4 gene for example, spans 4 windows. Larger genes spanning more windows would be subjected to more tests, whereas smaller genes spanning only 1 window are tested only once. In genes that span more than 1 window, multiple testing becomes an issue. In the case of MAP4, because the gene's 9 rare causal variants all fall within the 2 windows  and SCAP (p =10−5) genes. Both methods failed to detect the other simulated true causal genes at more than a 10−4 level of significance. Both suffer from elevated type I error with roughly 6% of hits reaching levels of high significance .In this study, we analyzed the GAW18 data set using 2 FBAT-rare methods (v0 and v1) to assess their power to detect rare causal variants associated with complex diseases. Results from these tests show that the weighed v1 method has better detecting power than the v0 method  on 20 pedigrees provided by the GAW18, and our results indicated that weighted collapsing methods have more power than unweighted methods and inflated type I errors. We also applied a sliding-window approach to the same data sets. Although that approach tends to inflate the false-positive rates, it does significantly increase the power to identify some of the causal rare variants in GAW18 data.The authors declare that they have no competing interests.YYS, MX, and WG conceived of and designed the study. HZW, MX, and HQ performed data annotation and analysis. The manuscript was analysed by MX and written by MX, HZW, YYS, WG and HQ.All authors read and approved the manuscript.


Brassica napus. To investigate the genetic architecture of flowering time, a genome-wide association study (GWAS) of flowering time was conducted with a diversity panel comprising 523 B. napus cultivars and inbred lines grown in eight different environments. Genotyping was performed with a Brassica 60K Illumina Infinium SNP array. A total of 41 single-nucleotide polymorphisms (SNPs) distributed on 14 chromosomes were found to be associated with flowering time, and 12 SNPs located in the confidence intervals of quantitative trait loci (QTL) identified in previous researches based on linkage analyses. Twenty-five candidate genes were orthologous to Arabidopsis thaliana flowering genes. To further our understanding of the genetic factors influencing flowering time in different environments, GWAS was performed on two derived traits, environment sensitivity and temperature sensitivity. The most significant SNPs were found near Bn-scaff_16362_1-p380982, just 13 kb away from BnaC09g41990D, which is orthologous to A. thaliana CONSTANS (CO), an important gene in the photoperiod flowering pathway. These results provide new insights into the genetic control of flowering time in B. napus and indicate that GWAS is an effective method by which to reveal natural variations of complex traits in B. napus.Flowering time adaptation is a major breeding goal in the allopolyploid species  It was grown on 36.5 million ha and produced 72.7 million tonnes of seed worldwide in 2013 . Rapeseed is used not only as an edible oil but also as an industrial material for lubricants and biodiesel. Brassica napus is a recent allopolyploid species that evolved from natural hybridization between two diploid progenitor species, Brassica rapa  and Brassica oleracea , followed by chromosome doubling at least 10,000 yrs ago.2 It was domesticated as an oilseed crop only 400–500 yrs ago.4 According to the requirements of vernalization, B. napus can be divided into three different growth types: spring type, semi-winter type and winter type.Rapeseed , the key gene in the vernalization pathway,13 and BnCOa1 is orthologous to A. thaliana CO, the core gene in the photoperiod pathway.14Previous studies of the genetic architecture of flowering time in rapeseed were based on QTL linkage mapping using traditional molecular markers, such as restriction fragment length polymorphisms, simple sequence repeats, intron polymorphisms and sequence-related amplified polymorphism markers in bi-parental populations. Many QTLs related to the flowering time of 15 Genome-wide association studies, also called association mapping or linkage disequilibrium (LD) mapping, can be used to study millions of polymorphisms segregating in natural populations, which can be tested for their effects on a phenotype of interest.16 GWAS was first applied in the study of human diseases.17 With the development of sequencing technologies, GWAS has been successfully applied to the genetic dissection of complex traits in plants, such as A. thaliana,18Oryza sativa,19Zea mays20 and B. napus.22 Compared with linkage mapping, GWAS takes less research time, because it is not necessary to create mapping population, and it takes full advantage of ancient recombination events to identify the genetic loci underlying traits at a relatively high resolution.25Linkage mapping is restricted to allelic diversity and has limited genomic resolution.B. napus cultivars and inbred lines was genotyped with the Brassica 60K Illumina Infinium SNP array. Flowering times of the panel were investigated in eight different environments. The objectives of this study were to (i) determine the extent of LD in the population, (ii) dissect the genetic architecture of flowering time in B. napus and (iii) investigate the genetic control of the variation in flowering time in different environments.In this study, a diversity panel consisting of 523 2.2.1.B. napus cultivars and inbred lines, was used for association analysis in this study (Supplementary Table S1). These germplasms originated from 10 countries on 4 continents, and most came from China. These accessions included winter oilseed rape (OSR) (40), semi-winter OSR (433) and spring OSR (44) (Supplementary Table S1). The self-pollinated seeds for each accession were planted in the experimental field with a randomized complete block design of three replications in eight natural environments at five different locations. Each plot contained two rows, with 12 plants in each row and 20 cm between plants within each row and 30 cm between rows. They were sown at the end of September or the beginning of October and harvested the following May. The eight natural environments were E1 , E2 , E3 , E4  and E5  in the 2012–13 growing seasons; and E6 (Wuhan), E7 (Chongqing) and E8 (Nanjing) in the 2013–14 growing season. The eight environments were semi-winter growing environment and the winter mean temperatures in the eight environments ranged from 0.8–7.7°C to 4.5–12.2°C (Supplementary Table S2).A diversity panel, consisting of 523 2.2.www.eXtension.org/pages/61006, 20 November 2015, date last accessed) based on a linear model.26Flowering time data were recorded as the number of days from the sowing day to the day 25% of the plants had at least one open flower in one plot in each environment. Flowering time was investigated for three replicates in E1, E5 and E6 and was investigated for only one replicate in the other five environments. Flowering time of each accession was defined as the average of the three replicates in the same environment. The coefficient of variation of flowering time (FT-CV) was used as a derived trait of environment sensitivity for each accession across the eight environments. FT-2013/2014 is the ratios of flowering times of the 2012–13 growing season to the 2013–14 growing season in the same location. SPSS software was used for the statistical analysis. The best linear unbiased prediction of flowering time (FT-BLUP) for each line in the eight environments was calculated using an R script  ≥0.05 and homozygous genotype frequency cannot be zero. The probe sequences of the SNP array were used to perform a BLAST search against the B. napus Genomes Browser . They were regarded as non-specific markers when BLAST matched to two or more locations in the reference genome. SNP markers used for LD analysis and association analysis were filtered with the following steps: (i) non-specific markers were excluded; (ii) markers that were not up to these standards of quality control for SNP data were eliminated; (iii) markers that did not have specific physical location information were excluded. SNPs that were selected for assessing population structure and relative kinship were filtered using the above first two steps.Genomic DNA for genotyping was extracted from leaf tissues collected from three plants of each accession by a modified cetyltrimethylammonium bromide method.2.4.K value, as a putative number of populations set from 1 to 10, was obtained with five independent runs. The length of the burn-in period and number of MCMC replications after burn-in were set to 50,000 and 100,000, respectively. The true k value was determined by the log probability of the data (LnP(K)) and an ad hoc statistic ΔK, based on the rate of change in LnP(K) between successive K values.28 The Q matrix was the result of the integration of the cluster membership coefficient matrices of replicate runs from STRUCTURE by the CLUMPP software. Principal component analysis (PCA) was also used to assess the population structure. PowerMarker version 3.25 was used to calculate genetic distances among varieties by the method of Nei's genetic distances.29 After double centring, distance matrices were used to obtain eigenvectors in NTSYSpc version 2.1. The relative kinship matrix was calculated using SPAGeDi software, and all negative values between two individuals were set to 0. The parameter r2 was used to estimate LD by TASSEL version 4.0. The polymorphism information content (PIC) of the SNP markers was estimated using PowerMarker version 3.25.30STRUCTURE 2.3.4 software was used to estimate the population structure with a Bayesian Markov Chain Monte Carlo model (MCMC). Each 2.5.31 The association analysis was performed with models by TASSEL version 4.0. The general linear model (GLM) included the naïve model that did not control for population structure and kinship; the Q model controlled the population structure using the Q matrix from STRUCTURE software to identify populations; the PCA model controlled the population structure using the top two principal components (PCs) from PCA to assess populations. The mixed linear model (MLM) included the following: the K model controlling kinship using the kinship matrix from SPAGeDi software to assess inter-individual relative kinship; the Q + K model controlling population structure with the Q matrix and kinship with the kinship matrix and the PCA + K model controlling population structure and kinship using the top two principal components and the kinship matrix, respectively. The Bonferroni test (0.05/number of tests) criterion is typically a very strict threshold;32 therefore, negative log (0.05/n) was used as a threshold for significance of associations between SNPs and traits, where n was the total number of SNPs used in the association analysis. In this study, the threshold was 5.6  ≈ 5.6). Quantile–quantile plots were created with a negative log value of the expected P-value from the genotype–phenotype association and the expected P-value from the assumption that no association exists between genotype and phenotype.Population structure and kinship were used to correct for false positives.3.3.1.Supplementary Fig. S1). The shortest average flowering times was 151 days in E5, and the longest was 168 days in E8 . These SNP markers were not evenly distributed across the whole genome. C9 had the lowest SNP marker density of one SNP per 77 kb, and A10 and C4 had the highest marker density of one SNP per 20 kb. The mean PIC values of the A subgenome and C subgenome were 0.3052 and 0.2974, respectively, and PIC values for each chromosome ranged from 0.2781 to 0.3219 (Table r2 (the squared pearson correlation coefficient) between all pairs of SNP markers. In the association panel, the LD decay of B. napus extending over a large distance was 6.5 Mb, where r2 = 0.1. The A subgenome and C subgenome were 1.2 and 7.8 Mb, respectively, and C subgenome LD was significantly higher than that of the A subgenome  value increased continuously with the increase of K from 1 to 10, and there was no obvious inflexion point. However, the most apparent change in LnP(K) appeared when K increased from 1 to 2, and the highest ΔK value was observed at K = 2 . Hence, the population could be divided into two clusters, P1 and P2 . In addition, PCA was used to assess genetic variation in the panel. The top two PCs explained 44% of the genetic variation, and P1 and P2 formed clear clusters based on the two PCs  was >0.75. In our study, these SNPs were considered to be the same QTL. These significant SNPs constituted 35 QTLs, which were distributed on 14 chromosomes across the B. napus genome and explained 5.28–15.75% of the phenotypic variation  with corresponding SNPs associated with flowering time (Supplementary Table S4). The closest distance between the candidate genes and significant SNPs was ∼6 kb. Twelve genes were within 100 kb of their corresponding significant signals and included genes orthologous to CO, FLC, VERNALIZATION INSENSITIVE 3, and SHORT VEGETATIVE PHASE .Our research found that the LD decay of ce Table , and pre10P > 5.6) was found in Changsha. Twenty-four SNPs were found to be associated with temperature sensitivity, and six SNPs associated with environment sensitivity were also associated with temperature sensitivity. The most significant SNPs associated with environment sensitivity and temperature sensitivity were found near Bn-scaff_16362_1-p380982, located at 43.7 Mb of chromosome C9 . Bn-scaff_16362_1-p380982 was also associated with flowering time in E6 ,36 1–100 Kb (maize)39 and 250 kb .40 These results reveal that the LD decay in B. napus is higher than that in other species, and the evolutionary time and mating system may be the main reasons for this difference. Mutation provides the raw material for producing polymorphisms that will be in LD, and recombination is the main phenomenon that weakens intrachromosomal LD.41Brassica napus is a recent species that was formed ∼10,000 yrs ago.1 As such, there has been limited time for B. napus to accumulate more mutations and undergo restructuring events. Furthermore, B. napus is often cross-pollinated; fertilization events are approximately one-third cross-fertilization and two-thirds self-fertilization.42 Self-fertilization causes populations to become composed of homozygous individuals, and high levels of homozygosity limit the effectiveness of recombination.43 The comparatively high resolution provided by association mapping is dependent upon the structure of LD across the genome.24 The high level of LD may make it hard to get a high-resolution result by association mapping. In B. napus, GWAS has been proved to be an effective tool in fine mapping of complex traits in a population which has the level of LD similar to our population.22 However, the resolution provided by association study will be higher in the population with more diverse germplasm bases.In a population of 192 inbred lines of B. napus has been improved by intentional introgression of genomic components from Chinese B. rapa.44 The A subgenome of B. napus is from European B. rapa, and Chinese B. rapa differs from European B. rapa.45 Therefore, the introgression into B. napus from Chinese B. rapa significantly increased the genetic diversity of the A genome. The LD of chromosome A8 decayed significantly slower than that of other chromosomes in the A subgenome. A similar result was found in previous studies.34BnaA.FAE1, which has been cloned and confirmed as the key gene controlling the content of erucic acid in rapeseed, is on chromosome A8.47 The strong artificial selection in the process of breeding is probably an important cause of longer LD decay distances on chromosome A8.The average PIC value of the A subgenome was slightly higher than that of the C subgenome. This result is consistent with the finding that the A subgenome LD decayed in a relatively shorter distance compared with the C subgenome, meaning that the genetic diversity in the A subgenome is higher than that in the C genome. In our association panel, the majority of accessions were from China. Chinese 4.2.33 Inter-specific crosses and hybridization between diverse germplasms from different countries were used to improve adaptation to the local environment and improve quality after B. napus spread to Australia, Canada, Japan and China.50 This spread resulted in introgression between germplasms of different countries. Moreover, there has been limited time for B. napus to undergo domestication after it was spread to different countries. Therefore, it is difficult to completely classify the association population according to geographical origins.This association population was classified into two subpopulations, but they were not completely separated according to geographical origin. In previous rapeseed association mapping panels, it is also hard to completely separate rapeseed lines according to geographical origin.Brassica germplasm.51 This approach was designed before the B. napus ‘Darmor-Bzh’ genome52 was released. Brassica napus is an allotetraploid species, with some SNPs from homologous sequence variants (HSVs) and paralogous sequence variants (PSVs). Previous research has found that 87.5–91.2% of the polymorphisms were from homologous genes from the two subgenomes in B. napus.53 HSVs and PSVs will lead to genotyping errors of the association panel, which may cause false positives in subsequent association mapping. Hence, excluding SNPs not in a single MEGABLAST hit by BLAST analysis of probe sequences against the reference genome will eliminate interference from HSVs and PSVs.The Brassica 60K Illumina Infinium SNP array was developed by an international consortium preferentially using single-locus SNPs identified from genomic and transcriptomic sequencing in genetically diverse 54 Many genetic markers appear to be associated with phenotype. In fact, these genetic markers simply capture the genetic relatedness among individuals.55 Flowering time was particularly strongly correlated with geographic origins and population structure in Z. mays and A. thaliana.57 The trait and polymorphism(s) were associated very strongly when population structure was ignored, but the association disappeared when structure was considered.57 As described in Fig. P-values. The MLM model, including the K model, PCA + K model and Q + K model, can markedly reduce inflation of P-values. Therefore, P-values were serious inflated when kinship was ignored. This indicates that relative kinship within the population probably is one of the major factors resulting in false positives in our association study.Genotype–phenotype covariance can lead to spurious associations.4.3.60 and seven SNPs near,10 the confidence intervals of QTLs identified in previous studies based on linkage analysis (Supplementary Table S6). There were 11 SNPs allele frequencies that showed significant difference between spring OSR group and winter OSR group (Supplementary Table S7). These SNPs corresponding candidate genes included some important vernalization-related orthologous genes, for example, BnaA10g22080D, BnaA02g08140D and BnaC09g41500D . BnaA10g22080D was the only candidate gene in the 300 kb range of the three SNPs Bn-A10-p14914898, Bn-A10-p15022346 and Bn-A10-p15106056, and was in the same location as BnFLC.A10.61 There was only one amino acid difference in the amino acid sequences of BnaA10g22080D and BnFLC1, and expression of BnFLC1 in A. thaliana delayed flowering significantly relative to untransformed Ler.13BnaA10g22080D is likely a functional allele related to vernalization. In addition, the remaining SNPs that have not been identified previously in linkage analysis may be novel and important QTLs related to flowering time; they should be verified by other methods in future research.Twelve SNPs associated with flowering time were located in,5 The temperature and photoperiod of different regions have significant differences, and there are also significant differences between the temperatures at the same location in different years. Considering the influence of environmental factors on flowering, the dates of flowering time in the eight different environments were separately analysed with association mapping. BLUP minimized the impacts of different locations and years on flowering time, and conversely, the derived trait of environment sensitivity highlighted these impacts. In the same location, the average temperatures of 2013–14 growing season were higher than that of 2012–13 growing season (Supplementary Table S2). Therefore, the ratio of flowering times between 2 yrs in the same location was regarded as a derived trait of temperature sensitivity. Six SNPs associated with environment sensitivity were also associated with temperature sensitivity . This result suggests that a particular factor affecting flowering times in different years in the same location may have been the major factor that led to differences in the flowering times in the eight environments. Temperature is one of the major environmental factors, but other factors affecting the flowering time could not be ruled out and should be studied in future research. Deep insight into the genetic factors and environmental factors influencing flowering time in different germplasms has a large application potential in rapeseed breeding and cultivation. The BnaC09g41990D orthologue of A. thaliana CO is only 13 kb away from the common significant association signal of environment sensitivity and temperature sensitivity. The temporal and spatial regulation of CO is key to the photoperiod-dependent induction of flowering, and recent research has found that CO protein stability is also affected by temperature.62 The TARGET OF EAT1 (TOE1) proteins interact with the activation domain of CO proteins and inhibit CO activity,63 and expression of TOE1 was reduced at 23°C compared with levels at 16°C.64 CO degradation by HIGH EXPRESSION OF OSMOTICALLY RESPONSIVE GENE 1 is increased under low temperature conditions (4°C).66BnCOa1, BnCOa9, BnCOb1 and BnCOb9 are orthologous to the Arabidopsis CO gene and were isolated from a pair of homoeologous loci in each of two B. napus lines displaying different flowering times. BnCOa1 has been shown to rescue the co-2 mutation in Arabidopsis.14 BLAST analysis showed that BnaA10g18430D and BnCOa9, and BnaC09g41990D and BnCOb1 have the same amino acid sequences. BnaA10g18430D and BnaC09g41990D were shown to have 98.7 and 94.3% identity, respectively, to BnCOa1 at the amino acid level. Given the above data, BnaC09g41990D and BnaA10g18430D are important candidate genes that may control B. napus flowering time using photoperiod and temperature.Flowering time is under the control of diverse environmental stimuli, such as temperature and photoperiod.Supplementary data are available at www.dnaresearch.oxfordjournals.org.National High Technology Research and Development Program of China (Grant No. 2012AA101107), 948 Program of Ministry of Agriculture of China (2011-G23), the National Basic Research Program of China (2011CB109300) and Natural science Foundation of Hubei province Key program (2014CFA008). Funding to pay the Open Access publication charges for this article was provided by the National High Technology Research and Development Program of China (Grant No. 2012AA101107).This work was supported by the


The main objective of the study was to find combinations of genetic variants significantly associated with bipolar disorder. In a previous study of bipolar disorder, combinations of three single nucleotide polymorphism (SNP) genotypes taken from 803 SNPs were analyzed, and four clusters of combinations were found to be significantly associated with bipolar disorder. In the present study, combinations of four SNP genotypes taken from the same 803 SNPs were analyzed, and one cluster of combinations was found to be significantly associated with bipolar disorder. Combinations from the new cluster and from the four previous clusters were identified in the genomes of 209 of the 607 patients in the study whereas none of the 1355 control participants had any of these combinations in their genome. In a previous study of bipolar disorder, we analyzed 803 SNPs belonging to genes related to signal transmission in the brain . CombinaThe first question is whether combinations of four SNP genotypes taken from the same 803 SNPs can reveal more clusters of combinations associated with bipolar disorder? Because the theoretical number of combinations of four SNP genotypes is 1,392,791,776,200, the computational challenge remains considerable, and here we report a way to give a partial answer to this question.The second question is whether some of the 208,699,590 combinations of three SNP genotypes found exclusively in control participants can be considered as protective or risk reducing regarding bipolar disorder?The Norwegian Scientific-Ethical Committees, the Norwegian Data Protection Agency, the Danish Scientific Committees, and the Danish Data Protection Agency approved the study. All patients gave written informed consent prior to inclusion in the project. Patients, genes, SNP selection, and genotyping have previously been described in detail .Screening for all combinations of two SNP genotypes and all combinations of three SNP genotypes taken from 803 SNPs were performed by array-based mathematical methods where data are represented geometrically, hereby facilitating ultrafast parallel processing . HoweverFrom the combinations of four SNP genotypes those occurring exclusively in patients were extracted, in order to analyze whether some of them were significantly associated with bipolar disorder. A combination common for many patients is more likely to be associated to bipolar patients than a combination common for few patients, so permutation tests were performed for combinations of four SNP genotypes that were found in 15, 16 or17 patients. (No combination was common for 18 or more patients). The permutation tests showed that no combination of four SNP genotypes was significantly associated with bipolar disorder.A cluster is defined as a group of combinations where all the combinations contain at least one SNP genotype which is the same in all the combinations. The combinations of four SNP genotypes found exclusively in patients were organized into such clusters. The patients belonging to a cluster are those that in their genome have one or more of the combinations in the cluster. As a cluster with many patients is more likely associated to bipolar disorder than a cluster with few patients, permutation tests were performed on clusters with many patients.Chi square tests were used as a tool to obtain a selection of combinations of four SNP genotypes small enough to be handled by the methods used to analyze combinations . From thThe highest number of patients belonging to a cluster was 73 in the original data set. In 1000 permuted data sets it was counted how often clusters with 73 or more pseudo patients were found. If such clusters were found N times, the p value is N/1000.All the 208,699,590 combinations of three SNP genotypes found exclusively in control persons were analyzed by the same methods as those used to analyze combinations of three SNP genotypes found exclusively in patients .4 = 1,392,791,776,200. Because of the computational burden, it was not possible to analyze how many of these combinations were present in the 1355 controls and 607 bipolar patients. Instead a selection of combinations of four SNP genotypes was analyzed. The selection was based on statistics as described in Materials and Methods. From the selected group of combinations of four SNP genotypes, those that occurred exclusively in patients were extracted. Using permutation tests it was found that none of these combinations were significantly associated with bipolar disorder. However, among these combinations, a cluster containing 16 combinations was found to be significantly associated with bipolar disorder . The 16 combinations are shown in Theoretically the number of combinations of four SNP genotypes taken from 803 SNPs is 803!/4!(803–4)! × 3For all other clusters it was found that similar clusters occurred more than 50 times in the 1000 permutations.In the previous study  208,699,The genetic basis for polygenic disorders is combinations of genetic variants, if a disorder shows genetic homogeneity this basis consists of only one combination. If the disorder shows genetic heterogeneity several combinations of genetic variants can be basis for the disorder. A combination of genetic variants that is the basis for a polygenic disorder has never been described, probably because analyses of combinations of genetic variants constitute computational and statistical challenges due to the large number of possible combinations, even with moderate numbers of genetic variants . In the In order to deal with the large number of combinations the statistical analyses can be restricted to the combinations found exclusively in patients, because the chances of finding combinations significantly related to a disorder may be larger in this group of combinations. A further reduction in the number of the patient specific combinations can be obtained by extraction of those combinations that are common to many patients instead of those that are common to few patients.However, all these methods cannot handle all the combinations of four SNP genotypes taken from 803 SNPs, not to mention the number of combinations of more than four genetic variants taken from studies where thousands of genetic variants have been analyzed. In the present study we have attacked this problem by the use of a selection procedure where not all, but only some combinations have been analyzed. The principle in the procedure is that the distribution between controls and patients for all the genetic variants are analyzed by chi square tests, and those with a low p value are selected. Instead of calculating all possible combinations of two genetic variants, only combinations where at least one genetic variant has a low p value are looked at. And the same principle is used with combinations of three and four genetic variants. By such stepwise selections it is possible to analyze combinations of two, three and four genetic variants, but the cost is that some combinations associated with bipolar disorder but with p values above the threshold may remain undetected. In large data sets as those from genome wide association studies much lower p values may be used in the selection procedure order to obtain numbers of combinations that are manageable. Also biological criteria could have been used in the selection procedure if, e.g., we had reasons to believe that genes for potassium ion channels were particularly important, combinations containing SNP genotypes from such genes could have been used in the selection procedure.The use of the selection procedure in the present study resulted in exactly the same four clusters of combinations of three SNP genotypes significantly associated to bipolar disorder, as found in the previous study, where all possible combinations were analyzed , showingAll combinations in a cluster contain a common SNP genotype, and in the cluster found in the present study , all 16 Protective or risk-reducing genes have been found for some diseases –17, raisIt is generally accepted that the genetic basis for polygenic disorders are combinations of genetic variants, but due to the high number of possible combinations it is difficult to find those that are the genetic basis. Using a procedure where only selections of combinations were analyzed it was possible to find clusters of combinations of SNP genotypes significantly associated to bipolar disorder. The combinations in the clusters were present in the genome of 35% of the patients, but absent in all control subjects. This finding indicates a role for combinations of genetic data in clinical work with diagnosis and estimation of risk of disease, but replication studies are warranted in order to further evaluate the relevance of combinations of genetic data. Such studies may be new, but combinations of genetic variants may also be analyzed in studies already published.S1 Table(TXT)Click here for additional data file.S1 Text(DOCX)Click here for additional data file.


Standard statistical approaches for prioritization of variants for functional testing in fine-mapping studies either use marginal association statistics or estimate posterior probabilities for variants to be causal under simplifying assumptions. Here, we present a probabilistic framework that integrates association strength with functional genomic annotation data to improve accuracy in selecting plausible causal variants for functional validation. A key feature of our approach is that it empirically estimates the contribution of each functional annotation to the trait of interest directly from summary association statistics while allowing for multiple causal variants at any risk locus. We devise efficient algorithms that estimate the parameters of our model across all risk loci to further increase performance. Using simulations starting from the 1000 Genomes data, we find that our framework consistently outperforms the current state-of-the-art fine-mapping methods, reducing the number of variants that need to be selected to capture 90% of the causal variants from an average of 13.3 to 10.4 SNPs per locus (as compared to the next-best performing strategy). Furthermore, we introduce a cost-to-benefit optimization framework for determining the number of variants to be followed up in functional assays and assess its performance using real and simulation data. We validate our findings using a large scale meta-analysis of four blood lipids traits and find that the relative probability for causality is increased for variants in exons and transcription start sites and decreased in repressed genomic regions at the risk loci of these traits. Using these highly predictive, trait-specific functional annotations, we estimate causality probabilities across all traits and variants, reducing the size of the 90% confidence set from an average of 17.5 to 13.5 variants per locus in this data. Genome-wide association studies (GWAS) have successfully identified numerous regions in the genome that harbor genetic variants that increase risk for various complex traits and diseases. However, it is generally the case that GWAS risk variants are not themselves causally affecting the trait, but rather, are correlated to the true causal variant through linkage disequilibrium (LD). Plausible causal variants are identified in fine-mapping studies through targeted sequencing followed by prioritization of variants for functional validation. In this work, we propose methods that leverage two sources of independent information, the association strength and genomic functional location, to prioritize causal variants. We demonstrate in simulations and empirical data that our approach reduces the number of SNPs that need to be selected for follow-up to identify the true causal variants at GWAS risk loci. Recent breakthroughs in high throughput genotyping technologies have ushered in the era of genome-wide association studies (GWAS) that have reproducibly identified thousands of genetic variants associated to many diseases and complex traits Many statistical approaches have been introduced for fine-mapping ranging from a simple ranking of marginal association statistics to Bayesian approaches that integrate elaborate priors Large-scale initiatives such as The Encyclopedia of DNA Elements (ENCODE) In this work we introduce PAINTOR (Probabilistic Annotation INTegratOR), a framework to combine external functional annotations  with genetic association data (the strength of association between genetic variants and the phenotype) to improve the prioritization of causal variants in fine-mapping studies. As compared to existing approaches that only rely on the strength of association between genotype and phenotype http://bogdan.bioinformatics.ucla.edu/software/paintor/.We use extensive simulations starting from the 1000 Genomes data to show that our approach improves resolution of statistical fine-mapping and is superior to existing frameworks. In our simulations of a trait with a heritability of To illustrate PAINTOR, consider the case of two risk loci that are fine-mapped through sequencing to elucidate the causal variant(s) driving the phenotype . The obsNumerous approaches for fine-mapping have been proposed, ranging from methods that require individual genotype data to methods that take as input summary association data and integrate functional annotations see . We usedants see . We compWe find that prioritizing variants using PAINTOR posterior probabilities achieves superior accuracy over existing methodologies see . Our appHaving established that PAINTOR increases fine-mapping accuracy over existing methods in simulations, we next explored the gain in performance attributable to having access to functional annotation data. We find that prioritizing variants using PAINTOR with functional data increases accuracy at all significance thresholds. For example, in order to find  of all causal variants one needs to select an average of  SNPs per locus if integrating functional data as opposed to  if excluding annotation data. We note that our approach that does not empirically estimate the prior, but uses the known prior information does not lead to superior performance over PAINTOR in these simulations see  reflectiWe next sought to determine at what types of loci is functional prior data providing the biggest increase in accuracy. Loci where the association signal is strong  do not gain much from integration of functional annotation data, with the number of SNPs required to find 90% of the causal variants decreasing by only 6.5%. On the other hand, at loci where the association signal is weak  we observe a 21.4% decrease in the total number of SNPs to be followed-up to find 90% of all causal variants see . This suIt is not guaranteed that the true causal variant will be present in the fine-mapping data set due to technical reasons (e.g. capture sequencing technology or imputation accuracy). To explore this scenario, we simulated fine-mapping data sets at a locus 100 Kb in size after which we masked the true causal(s) from the data see . To measρ-level causal set as the set of top SNPs (rank-ordered based on probabilities) across all fine-mapping loci that consume an total posterior probability mass. We observe a reduction in the number of SNPs within the 90%, 95% and 99% confidence sets when using functional annotations as compared to no functional data  see .A vast resource for functional annotations is the ENCODE project Although PAINTOR (and previous methods) provide a quantification of the probability of each variant to be causal that can be used to rank variants based on their plausible causality, it remains unclear how to choose the number of variants to test in functional assays. The optimum number is constrained by the budget of the study and by an implicit cost to benefit ratio for selecting the optimal number of SNPs to be followed up. We propose a framework that assumes that every causal variant identified adds a benefit  to produce a prioritization of plausible causal SNPs for these phenotypes. We used the GWAS hits reported by Teslovich et al. Having identified functional annotations that are relevant to the four traits of interest see , we deviRecent efforts by large consortia such the ENCODE have provided a genomic map of regulatory regions and have shown that GWAS associated variants are preferentially enriched within these regions. In this work, we propose a principled approach to unifying these genomic features with the standard association signal to improve the localization accuracy in fine-mapping studies. Our method relies on empirical data to select trait-specific genomic annotations, thus removing the need for ad-hoc selection of relevant functional annotations a priori. Through simulated and real data results, we have shown that our integrative framework is able to reduce the number of variants that need to be investigated to identify causal variants that alter risk of disease.Our method shares similarities to recent integrative approaches proposed in the context of GWAS Several hierarchical Bayesian methods have been developed that combine prior information with genomic association data to help prioritize variants in various contexts We have shown that PAINTOR can unbiasedly estimate enrichment of causal variants in different functional elements on the basis of summary association data alone. This may prove to be particularly important as access to individual genotype data is more cumbersome than summary-level statistics. The unbiased nature of the estimation procedure may provide clues to the genetic basis of common traits. For example our results suggest that although coding variants are more likely to be causal than regulatory variants, the majority of the genetic variation contributing to the trait at these risk loci may lie within regulatory as opposed to coding regions due to the larger number of variants residing in regulatory regions. This is consistent with recent work that concluded that variants in regulatory regions show a higher contribution to traits than coding variants, however, such an analysis required individual level data One interesting implication of our results is that while higher-order functional data is very useful for gleaning insight into to the genetic architecture of human diseases genome-wide In this work we have applied our framework to known risk loci identified in GWAS in the search for plausible causal variants. As future work, our approach could be extended to risk loci that do not pass a genome-wide stringency, potentially leading to discovery of novel risk loci. Additionally, risk loci for related traits that are known to share a genetic basis could potentially be combined, leading to an increase in power to identify variants that contribute to both traits. Finally, we anticipate that the approximations of the non-centrality parameters could be handled in a more principled fashion using a Bayesian approach that integrates a prior distribution of effect sizes. We leave a thorough investigation of these directions as future work.A standard approach to model the strength of association of genotype to phenotype is through the Z-score. For a continuous phenotype, the trait values are marginally regressed on each SNP and the corresponding Z-score is taken to be the Wald statistic  European samples, we used HAPGEN Once we established the causal SNPs, we used a linear model to simulate continuous phenotypes such that the causal SNPs aggregated to explain a fixed proportion of the phenotypic variance (ants see ). In parfine flag. Due to the fact that we fit linear models to obtain Wald statistics for each SNP, we were able to provide standard errors for the estimates of the prior variance. We segmented our input based on the individual loci as instructed in user manual, but provided a single file that contained all the fine-mapping SNPs so that fgwas could compute enrichment. The Guan and Stephens piMass which we ran using the flags and MCMC parameters given in the user manual as defaults . We used the posterior inclusion probabilities (PIPs) that had undergone Rao-Blackwellisation for prioritization due to the fact these had superior performance over naive PIPs. The R package implementing LLARRMA We compared our approach to a several of existing methods that can be used for fine-mappingWe explored whether integration of the location of tissue-specific regulatory and coding DNA regions could increase resolution in statistical fine-mapping. The ENCODE Due to the fact that we fit our model using maximum likelihood, a natural way to ascribe statistical confidence to the inferred parameters is to use a likelihood ratio test. For example, to calculate the significance of a single annotation, we can compare a fitted null model to a model that contains the annotation under consideration using the following test statistic: tion see .In addition to a point estimate for the enrichment of functional annotation, it would be useful to derive an estimate of the variance. Unfortunately, the complex structure of the likelihood makes it difficult to derive an analytically tractable parameter covariance estimator. However, since we assume fine-mapping loci to be independent, we propose to use bootstrapping (i.e. re-sampling entire loci with replacement) and subsequently re-fitting the model see . We confThe budget of a fine mapping follow-up study constrains the total number of causal variants to be further examined for evidence of causality. This motivates approaches that, in addition to providing a prioritization of SNPs, also identify an optimal number of SNPs to be tested. We introduce here a benefit-to-cost framework for selecting the optimal number of SNPs for follow-up. Our framework assumes that every causal variant identified adds a benefit (B) while every selected variant is tested at a cost (C); therefore, the utility function we propose to maximize is U = B*Nc - C*Nt, where Nc is the total number of true causal variants identified from the total number of selected SNPs. A key parameter of the utility framework is the ratio of Publicly available GWAS summary data across four blood lipids phenotypes was downloaded from public access websites Figure S1Single locus fine-mapping using four different prioritization strategies. Using HAPGEN-derived genotypes from a randomly selected a 10KB locus on chromosome 1, we simulated 10,000 fine-mapping data over N = 2500 samples at a locus that explains 5% of variance in the phenotype. Each variant has a prior probability of 1/L  to be casual; the total variance was divided equally among variants when multiple causal variants were present. As previously observed, prioritization under the assumption of a single causal variant is identical to ranking based on p values at a single locus.(EPS)Click here for additional data file.Figure S2Contiguous annotations do not lead to appreciably different performance to randomly assigned annotations. Displayed here is the accuracy of enrichment estimation for a synthetic annotation that contains 8-fold depletion to 8-fold enrichment of causal variants across simulations of fine-mapping data sets over 100 loci. We enriched causal variants in an annotation that spanned a block 1/3 of the size of the locus and simulated with annotation effect sizes such that in expectation, we attained approximately 100 causal variants while maintaining enrichment at a fixed point. We used the standard simulation parameters, fixing the variance explained by these 100 loci to 0.25 and using erge see .(EPS)Click here for additional data file.Figure S3Selection of optimal fine-mapping set according to an utility function. Using our standard simulation parameters ((EPS)Click here for additional data file.Figure S4Runtime scales exponentially as the number of causal variants integrated over increases. We assesed run-time within the context of our standard simulation framework (ten simulations per point) and varied the number of causal variants PAINTOR integrated over. These simulations were carried out on a single core of an Intel(R) Xeon(R) E5335 2.00 GHz CPU. As the results suggest, we are required in practice to restrict the number of causal variants to a small fixed constant (EPS)Click here for additional data file.Figure S5Performance using different strategies for approximating the non-centrality parameters (EPS)Click here for additional data file.Figure S6Overall performance with heterogenous SNPs effect sizes. To induce heterogeneity on SNPs, effect sizes of causal sites were drawn from an (EPS)Click here for additional data file.Figure S7Comparison of current methodologies using positive predictive value (PPV) as the metric (defined as: (EPS)Click here for additional data file.Figure S8Posterior probabilities for causality under the assumption of a single causal variant approximated from z-scores give indistinguishable performance to that of the Bayesian approach described in Maller et al. (EPS)Click here for additional data file.Figure S9QQ Plot of likelihood ratio test statistics for a single annotation. Using the standard simulation conditions see , we ran (EPS)Click here for additional data file.Figure S10Bootstrap standard deviations for different log2 enrichment values. Using the standard simulation conditions see , we ran (EPS)Click here for additional data file.Table S1Basic summary of fine-mapping methods assessed. We highlight the key contribution of our approach is that we can use PAINTOR to do fine-mapping with functional priors while modeling multiple causal variants directly from summary association statistics (Z-scores).(PDF)Click here for additional data file.Table S2Incorporating prior probabilities provides larger benefit when Z-scores at the causal SNPs are smaller. Here, we illustrate the efficacy of fine-mapping at loci where the p-value at the causal SNPs fall in either the top or bottom quartile of significance (as indicated by the absolute z-score).(PDF)Click here for additional data file.Table S3Performance of PAINTOR with and without integrating annotations if thresholding on the posterior probability . The objective function is given as ratio from the maximum objective at a cost to benefit ratio of 10.(PDF)Click here for additional data file.Table S4Imputation boosts estimates of enrichment/depletion. The original data set was imputed up to the HapMap. Using ImpG-Summary we further imputed Z-scores up to the 1000 genomes reference panel. We combined enrichment estimates across all 4 phenotypes and examined the tails of log2 enrichment distributions.(PDF)Click here for additional data file.Table S5LDL SNPs attaining PAINTOR posterior probabiliites (PDF)Click here for additional data file.Table S6TC SNPs attaining PAINTOR posterior probabiliites (PDF)Click here for additional data file.Table S7TG SNPs attaining PAINTOR posterior probabiliites (PDF)Click here for additional data file.Table S8Performance of PAINTOR as a function of sample size. We fixed the proportion of phenotypic variance explained in a simulated trait to (PDF)Click here for additional data file.Table S9Average number of SNPs that were well-imputed at the loci for the four lipid phenotypes. The top row corresponds to the average number of common SNPs in the 1000 Genomes reference panel at these loci. The bottom row corresponds to the average number of SNPs that were imputed with accuracy (PDF)Click here for additional data file.Note S1Comparison of methods for single locus fine-mapping and approximation of posterior probabilities from z-scores under the assumption of a single causal variant.(PDF)Click here for additional data file.


Brassica Infinium SNP array. Significant phenotypic variation was observed from 20 to 70°. As a result, 25 significant quantitative trait loci (QTL) associated with branch angle were identified on chromosomes A2, A3, A7, C3, C5, and C7 by the MLM model in TASSEL 4.0. Orthologs of the functional candidate genes involved in branch angle were identified. Among the key QTL, the peak SNPs were close to the key orthologous genes BnaA.Lazy1 and BnaC.Lazy1 on A3 and C3 homologous genome blocks. With the exception of Lazy (LA) orthologous genes, SQUMOSA PROMOTER BINDING PROTEIN LIKE 14 (SPL14) and an auxin-responsive GRETCHEN HAGEN 3 (GH3) genes from Arabidopsis thaliana were identified close to two clusters of SNPs on the A7 and C7 chromosomes. These findings on multiple novel loci and candidate genes of branch angle will be useful for further understanding and genetic improvement of plant architecture in rapeseed.Changes in the rapeseed branch angle alter plant architecture, allowing more efficient light capture as planting density increases. In this study, a natural population of rapeseed was grown in three environments and evaluated for branch angle trait to characterize their phenotypic patterns and genotype with a 60K  Brassica napus L. 2n = 4 × = 38, AACC genomes) is a widely cultivated oil crop throughout the world. Yield improvement and mechanized harvesting are extremely urgent recently for the demands of rapeseed producers in addition to the edible oil and biofuel industries  genome sequencing  mapping has become a powerful tool for identifying important genes associated with complex traits, which has been used with success in model and non-model plants  angle in model and other crops. For instance, s Lomax, . Auxin ms Lomax, , which iBrassica Infinium SNP array. The branch angle was measured in 2013–2014 at three environments. The SNPs in the array were in silico mapped to A and C genomes of Darmor-bzh B. napus genome “pseudomolecules” to obtain their hypothetical position. The aims were (1) to gain the population structure and genetic diversity in elite germplasms; (2) to detect QTL controlling branch angle and mine for elite alleles; and (3) to predict the candidate genes.In this study, a panel of 143 elite rapeseed accessions was analyzed by the 60 K A total of 143 rapeseed accessions were used for an association analysis in this study. According to the information from field observations, the accessions were classified to three different germplasm types, i.e., spring oilseed rape (OSR) (13), semi-winter OSR (124), and winter OSR (6). Based on their origins, 112 accessions originated from China, 24 from Oceania, 5 from Europe, 1 from North America, and 1 from India , Wuhan, China, during the 2013 and 2014 winter growing season and at Lu'an Experimental Station  in Anhui, China, during the 2013 winter growing season. In each environment, the experiment was conducted in randomized complete blocks with two replicates. Each plot contained three rows with 54 individuals, setting as 33 cm between rows and 11 cm between plants within each row, with a planting density of 270,000 plants/ha. All experiments were performed under local field management and cultivation conditions.In each plot, five typical plants were harvested for branch angle measurement at the mature stage. The branch angle (BA) was measured as the angle between the main stem and the branch. BA was scanned with a digital camera . The angle value from the images was obtained using AutoCAD software . The average BA value of five individual plants for each plot was calculated as the final phenotypic value. In addition, the best linear unbiased estimators (BLUPs) across all three environments were predicted by assuming fixed genotypic effects to minimize the effects of environmental variation. Finally, each environment and BLUP value was used as a phenotype for the association analysis.H2) was calculated as H2 = σg2/(σg2 + σgl2/n +σe2/nr), in which σg2, σgl2, σe2, r, and n represent the estimated variances for the genetic effects, genotype-environment interactions, random errors, number of replications and number of environments, respectively. The estimated variances for σg2, σgl2, and σe2 were obtained by ANOVA.Statistical analysis of the data was performed by using PROC MEANS in SAS software, Version 9.3 . Analysis of variance (ANOVA) was conducted by using PROC GLM to determine the effects of block, environment, genotype and genotype-environment interactions. Correlation coefficients were obtained by using PROC CORR. The Broad-sense heritability . Only the top BLAST hits with an E-value cut-off of 1E-15 against the pseudomolecules were retained, while BLAST matches to multiple loci with the same E-value were deleted. A final set of 34,469 high-performing SNPs was used for all the analyses.SNP mapping was performed as previously reported . Kinship (K) matrix used to compare all the pairs of the 143 accessions was calculated with 2434 informative SNPs with a MAF > 0.2 by using the SPAGeDi software package  ranging from 1 to 10. The optimal K-value was determined by taking the log probability of the data [LnP(D)] and an ad hoc statistical Δk based on the rate of change for LnP(D) between successive k-values as described by Evanno et al. (r2) for estimating the degree of LD between pair-wise SNPs (MAF ≥ 0.05) was calculated using the software TASSEL 4.0  ≥ 0.2] that were evenly distributed across the whole genome were selected to create the population structure inferred by using the STRUCTURE v2.3.4 software package  without controlling for Q and K, containing only the SNP that was tested as a fixed effect. The second model was a mixed linear model (MLM) where, in addition to testing the SNP, the population structure (Q) and relative kinship matrix were included as fixed and random effects, respectively. Analyses were performed by using TASSEL 4.0 software, for which the optimum compression and population parameters previously determined (P3D) variance component estimation were implemented to decrease the computing time for the large data set  = 4.5]. The threshold is 2.90 × 10−5 at a significant level of 1% after Bonferroni multiple test correction . Furthermore, we applied the false discovery rate (FDR) technique. We calculated an FDR q-value for each association test by using the software QVALUE  provided an estimate of the proportion of false positives among the significant associations. The significant value and the marker effect for each SNP were exported, and a Manhattan plot was generated in the R package qqman .The significance of associations between SNPs and trait was based on a threshold of R2) by using the lm function in R  for branch angle was calculated as 93.90%, demonstrating that branch angle in these rapeseed lines was conditioned primarily by genetic factors. The correlation coefficients for branch angle between environments were all relatively high .This observation indicated that branch angle in the 143 lines was relatively consistent across environments.The two-way ANOVA showed that differences among the lines in the branch angle were highly significant. This finding confirmed that a large number of genetic variation existed in the population. The effects from years and location were significant Table . The broSupplementary Table r2 was used to calculate LD. The genome-wide LD decay of A and C genome for rapeseed germplasms are shown in Figure r2 decayed to 0.2 when the average distance for A genome was 206 kb and r2 decayed to 0.2 when the average distance for C genome was 949 kb.To evaluate the extent of LD, k-value was observed at k = 2  from 1 to 10 showed that the most significant change in likelihood occurred when K increased from 2 to 3, and the highest Δ2 Figure , the 1432 Figure . By usin2 Figure . In addiThe 2434 informative SNPs with a MAF > 0.2 and little or no missing data were used to estimate the relative kinship in the set of 143 lines. As shown in Figure P < 2.90E−5) were detected for branch angle by using BLUP across three environments and an individual environment  orthologs were searched in the “pseudomolecules” of B. napus and one ortholog was found at 24.3 Mb of A7, which was 521 kb away from the peak SNP Bn-A07-p19977445. Aside from the Lazy and SPL14 genes, an auxin-responsive GRETCHEN HAGEN 3 (GH3) ortholog “pseudomolecules” of B. napus in 48.7 Mb of C7, which was very close (only 4 kb) to the peak SNP Bn-scaff-16110-1-p1940585.Notably, the B. napus germplasm lines was adopted for association mapping study. Significant natural phenotypic variation in branch angle was observed in rapeseed germplasms. In general, to unravel the genetic basis of trait variation, a number of traditional genome-wide phenotype-to-genotype approaches have been employed by LD association mapping. An association mapping study employs the large number of recombination events that occur throughout the entire breeding selection history of the mapping population, thereby allowing fine-scale QTL mapping  were detected for branch angle in three environments, and 25 significant SNP loci were further verified using BLUP model. Through the analysis of GWA, the markers detected in the environmental BLUPs value correlated significantly (P < 0.001) with branch angle, with phenotypic value effects between 16.60 and 18.93%. Exploring these associated markers provides a genetic basis to analyze branch angle variation in rapeseed.In this study, a panel comprising 143 B. napus accession lines can be largely divided into two sub-populations in STRUCTURE and compared with an association analysis from a previous study  orthologous, SPL14 (AT1G20980) and Auxin-responsive GH3 family protein (AT5G51470) genes, which were all relevant to angle formation in Arabidopsis thaliana.To account for the potential number of false positives, we implemented stringent quality control on the included polymorphisms, with conservative non-parametric testing and an adjusted statistical significance threshold. Our approach relied on natural variations in rapeseed, leading to a set of strong candidate genes by comparative genome method. A high degree of co-linearity and congruence in the Fatty Acid Elongation 1 (FAE1) and High Aliphatic Glucosinolate 1 (HAG1) gene locus, gene locus mutation occurs at a lower frequency in double-low rapeseed populations (Li et al., Rapeseed is an excellent model for association analyses because of the extensive architectural variation across its native range and its diverse germplasm collections through artificial selection. During rapeseed domestication and breeding process, breeders often focus on important characteristics such as oil content, biotic stress resistance, and quality for directional selection for greater oil yield and better quality, which were directly caused by an artificial selection gene locus mutation at a lower frequency. For example, in terms of oil and glucosinolate contents, and because of the artificial selection on The association of branch angle with increased plant productivity in rapeseed may be beneficial to lodging resistance and high-density field cultivation. This genetic analysis of branch angle and plant morphological characteristics was only based on one natural population. Therefore, the observed inter-trait and trait-marker associations must be confirmed in other rapeseed populations. Further evaluations of branch angle and plant morphology should be conducted under contrasting cropping density, and total seed yield measurements should be taken because the seed harvest index in addition to the plant growth and productivity are strongly affected by the cropping density.In this study, GWA mapping with corrections for the population structure were used to identify a number of novel loci and refine the map locations of known loci related to branch angle in rapeseed. This information not only demonstrates that GWAS mapping can be used as a powerful tool for dissecting plant architecture mechanisms in rapeseed but also provides valuable markers for breeding rapeseed cultivars with the ideotype. In addition, the candidate genes nearby these SNP loci represent promising targets for efforts to further identify causal variants and to clarify how the implicated genes affect branch angle in rapeseed.JL and QH conceived and designed the study. JL, WW, and DL conducted the experiments; DM and HW coordinated genotyping with SNP markers; LF and YL provided rapeseed lines; JL and WW analyzed and interpreted data, and prepared the manuscript; QH supervised the whole study; all authors reviewed and edited the manuscript.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.


As a result, information on recombination rates is critical for biological research. In this paper, we introduce a new extremely fast open-source software package (FastEPRR) that uses machine learning to estimate recombination rate  Genetic recombination exchanges genetic material, produces new haplotypes during meiosis, and plays a critical role in organismal evolution . In livihttp://ldhat.sourceforge.net/) with, most recently, a varying recombination rate model applied to calculate a composite likelihood . Second, we introduce a linear correction and demonstrate that estimates using FastEPRR are unbiased. Third, we propose a method  to take into account the effects of variable recombination rates within windows. Finally, as a test case, we analyze the 1000 Genomes phased OMNI data set , especially the frequency of singletons  each with a step length half their size , we can denote i-th region. To estimate (1)(2)Minimize (3)Maximize Of these, the first condition is easy to accept because recombination rate should be positive, and since File S1.When estimating recombination rate for a given window, we assume that this is constant. However, because this may not be correct, the effect of a variable recombination rate within a given window can be investigated by sliding others over it. For example, if we consider four overlapping sliding windows  based on To validate the performance of FastEPRR, we compared it to our earlier regression-based method (gam), as well as to the composite-likelihood method (implemented in LDhat). Estimates from these three methods are denoted complete program to calculate the likelihoods of all two-locus haplotype configurations, with a population mutation rate pairwise program to estimate the recombination rate.To estimate i.e., We studied cases with different sample sizes  was simulated using msms , and randomly selected We simulated neutral data using the coalescent simulator Hudson’s ing msms . To assei.e., To investigate potential bias due to the phasing process, we randomly paired simulated haplotypes to form genotypes . Following the method described above , we then obtained a genetic map at the 25-kb scale, finer than that at the 50-kb scale.To consider the effects of variable recombination rates within windows, we scanned each autosome with overlapping sliding windows (http://www.picb.ac.cn/evolgen/softwares/) along with the related genetic maps.FastEPRR is an R package (open source) that can run across a range of platforms once a standard environment has been installed. This software can be downloaded from our institutional website . We further investigated this issue and observed that the RMSE of Table S1), which suggests that the accuracy of It has been shown that examined , as a liain bias . When sathe same . When itTable S2), indicating that We then examined the correlation between ed cases , and shounbiased . Indeed,smallest .Because the rate of multiple hits is high in many viruses and bacteria  compared to the current population recombination rate  shows that the average Figure S5. Recombination rates show a large degree of along-chromosome variation in the YRI population , in agreement with previous findings , which means that Figure S7); comparing the We compared the Figure S6) as this provides the most accurate estimate for recombination rate. In this case, the Pearson correlation coefficients between the We also established another genetic map using Table S3). Computing time for the genome-wide analysis of the YRI, CEU, and CHB populations (using a sliding window length of 50 kb) was 66.3, 45.7, and 49.0 hr, respectively. Indeed, if a small computer cluster  was used, each analysis could be completed within less than 4 hr, and this time could be further decreased if the number of nodes were increased. FastEPRR will thus prove a very useful piece of software for the analysis of genome wide polymorphism data from large samples, for example the UK10K project  800 MHz processor using a single core . Our evaluation of the performance of FastEPRR with, and without, Figure S9), shows almost the same results in terms of means and the SD of estimated recombination rate. In agreement with previous work  to facilitate other studies and to promote FastEPRR as a useful, fast, and effective tool for creating genetic maps and studying recombination hotspots in the genomic era.Sample sizes are expected to increase dramatically as sequencing technologies advance and more and more organisms are investigated (