These candidate genes included three known ST genes  for QTN qSNK1 qSST5 and qSST9. Candidate genes showed significant phenotypic differences in ST traits were detected between or among 2–4 major haplotypes. Thus, our results provided useful materials and genetic information for improving rice ST in future breeding and for molecular dissection of ST in rice.To facilitate developing rice varieties tolerant to salt stress, a panel of 208 rice mini-core accessions collected from 25 countries were evaluated for 13 traits associated with salt tolerance (ST) at the germination and seedling stages. The rice panel showed tremendous variation for all measured ST traits and eight accessions showing high levels of ST at either and/or both the germination and seedling stages. Using 395,553 SNP markers covering ~372 Mb of the rice genome and multi-locus mixed linear models, 20 QTN associated with 11 ST traits were identified by GWAS, including 6 QTN affecting ST at the germination stage and 14 QTN for ST at the seedling stage. The integration of bioinformatic with haplotype analyses for the ST QTN lets us identify 22 candidate genes for nine important ST QTN ( As the most important staple food in Asia, a significant portion of rice crops are gworn along the coastal areas where rice paddy fields suffer various degrees of salinity. Salinity affects rice growth during all developmental stages from seed germination to reproduction3. With the development and spread of direct-seeding technology in many Asian countries, which requires high levels of germination and seedling establishment to achieve good harvests, salt tolerance (ST) at the seed germination and seedling stages has become a major rice breeding goal of these countries.Enormous environmental changes have brought negative impact on food crops in the world. Among these environmental factors, salinity is known to be able to inhibit plant growth and ultimately cause various degrees of crop yield losses4. Rice ST is a complex phenomenon trait both genetically and physiologically8. Thus, to efficiently exploit this genetic diversity of ST in breeding programs, it is important to identify quantitative trait loci (QTL)/quantitative trait nucleotides (QTN)/genes for ST at the seed germination and seedling stages so that marker-assisted breeding approach can be facilitated. Robin et al.9 used backcross population of IR62266-426-2 × IR60080-46A for mapping of osmotic related QTL. They identified 14 QTL on 8 chromosomes. Hossain et al.10 studied agronomic traits at the seedling and reproductive stages under saline condition and identified 16 QTL for salt tolerance, using an F2 population of Cheriviruppu × Pusa Basmati 1. Ghomi et al.11 identified 41 QTL affecting twelve physiological traits related to ST using 148 F2 population derived from Gharib (indica) × Sepidroud (indica). Sabouri et al.12 mapped 14 QTL in rice for physiological traits related to salt tolerance, using F2 population derived from Tarommahali and salt sensitive cv. Khazar.Most rice lines are sensitive to salt, particularly at the germination and seedling stage, but there is rich variability for ST among different rice accessions. It has been reported that some rice landraces such as Pokkali and Nona Bokra can withstand certain levels of salt stressSKC1 which encodes a member of HKT-type transporters and is involved in maintaining K+ homeostasis in the ST variety under salt stress13, OsCCC1 (cation-Cl− cotransporter) that OsCCC1 is reportedly involved in K+ and Cl− transport and plays a significant role in K+ and Cl− homeostasis and rice development14. OsEATB is also a cloned gene associated with tillering and panicle branching from rice variety 9311 which was down-regulated under salinity15. Other cloned ST genes included OsMAPK33 whose over-expression under salinity increased Na+ uptake, suggesting its negative role in ST16, and OsNHX1, a Na+/H+ antiporter of rice17 whose expression in roots and shoots increases under high NaCl and KCl.In addition to genetic analyses of ST by QTL mapping, several QTL genes for rice ST have been cloned. These included 18. Recently, natural population has been widely used in identifying QTL/QTN for complex traits, which have some advantages over the bi-parental populations20. Emon et al.21 used rice landraces and found 220 different markers associated with ST, eight of which were sequence-tagged-site markers developed for genes SKC1, SalT and DST. Using 220 rice accessions, Kumar et al.22 identified 20 SNPs significantly associated with Na+/K+ ratio, which explained 5–18% of the phenotypic variance. Negrão et al.23 targeted several markers involved in Na+/K+ ratio maintenance and found the transmembrane domain interaction of OsHKT1;5 and P140A in ST using 392 rice lines. Platten et al.24 used 103 rice accessions for mining alleles at OsHKT1; 5 locus and identified seven major and three minor alleles for Na+ in shoots at the seedling stage. Mishra et al.25 studied the association of natural genetic variations and haplotype distribution in rice for salt responsive candidate genes and found 22 salt responsive candidate genes for different ST phenotypes and haplotypes were identified in the Indian germplasms. Wang et al.26 used six flowering time related traits in Arabidopsis thaliana and improved the power of QTN detection in GWAS.To date, large numbers of ST QTL have been mapped in rice, but most were identified by using bi-parental segregating populations involving a limited number of parents, which is unlikely to reveal the whole genetic variation for ST in rice germplasmsIn this study, we used 208 diverse rice lines collected from 25 countries and 700 K high-density SNPs to conduct an association analysis to identify candidate genes and haplotypes associated with ST of rice and to reveal the genetic relationship between ST at the germination and seedling stages. The results provide valuable insights into the genetic basis of ST in rice that could be important for rice production and improvement.27. FL478 and IR29 were used as the tolerant and sensitive checks, respectively29. For the nomenclature of the panel, accessions/lines of unknown country origin or with less than five samples from any single country were coded as CC, while the rest were coded with their respective country names, i.e. CH (China), Ind (India), Ban (Bangladesh), Phi (Philippines), Tha (Thailand), Tai (Taiwan) and Sri (Sri Lanka), etc. with their core collection serial numbers. As previously indicated27, two subgroups of the 219 associations were found by the 3-dimension principal component analysis (PCA) plot  and seedling length (SL) were measured for all geminated seeds of each genotype on the 10th day after soaking.Ten healthy seeds of each accession were selected and placed on to two filter papers soaked with 10 ml 100 mM NaCl in a petri plate for screening ST at the germination stage. For the controlled experiment, the same number of seeds of each line was placed on the filter papers soaked with 10 ml distilled water in a petri plate. All petri plates were incubated under the controlled conditions in the growth chamber with 25 ± 2 °C temperature, a 12-h light period and 60% moisture. The petri dishes were arranged in a completely randomized design with two replications for each accession. Seed sprouting and germination were recorded on daily basis. At 10 days after soaking, the final germination rate (GR) was calculated for each genotype31. The seeds were surface sterilized with 5% fungicide (sodium hypochlorite) solution for 20 minutes and rinsed well with distilled water. Seeds were soaked for 48 h and one healthy germinated seed was placed in per hole, ten holes were used for per genotype. To recover the radical and plumule, normal tap water with pH 5 was used in the containers for two days. At the 3rd day, saline solution with 70 mM and nutrients were applied, which is 50% of the actual stress. At the 6th day, the saline solution was raised to 140 mM and nutrients were used in the containers32. Nutrients solution pH (5.1 to 5.5) and glasshouse conditions were maintained on a regular basis. The solutions were changed every 5th day. When the susceptible check IR29 showed complete susceptibility to salinization, score for salt toxicity symptoms (SST) was evaluated according to the modified Standard Evaluation System (SES)33. Seedling survival days (SSD) were recorded on daily basis since first plant died. Finally, at the 16th day after salinization, whole plant samples of each accession were collected, dried, and then measured for root dry weight (RDW) and shoot dry weight (SDW) using a High Precision Digital Balance.The experiment for evaluating ST at the seedling stage was carried out in the glasshouse facility at Institute of Crop Sciences, the Chinese Academy of Agricultural Sciences (CAAS) in Beijing. The glasshouse conditions were set as 30–20 °C (day-night) and 60–65% relative humidity were regulated with a roof net, ventilation system and cooling pad. Plastic containers were prepared for the screening purpose and styrofoam sheets were used to fit inside of each container. Each styrofoam contains 10 × 13 holes, at the bottom of each styrofoam nylon net was stitched to prevent seeds from falling into the solution+ and K+ concentrations in the shoots and roots. The screening protocol of the second experiment was similar to the first experiment. The germinated seeds of 208 lines were sown in separate 96 wells PCR plates, with perforate wells at the bottom to facilitate the roots to have contact with the saline solution. Three replications were performed to minimize environmental errors. The shoots and roots were harvested and rinsed with distilled water several times after 8 d of salinization with 140 mM of NaCl. Samples were dried for 72 h at 60 °C in Blue Pard Oven (DHG-9240A), then weighed, and extracted in acetic acid (100 mM L−1) at 90 °C for 2 h. Root samples were diluted with distilled water as 1:11 for root Na+ concentration (RNC) and 1:2 for root K+ concentration (RKC) determination and shoot samples were diluted with distilled water as 1:24 for shoot Na+ concentration (SNC) and shoot K+ concentration (SKC) determination. Two replicates were performed per sample and the average value of the replicates was taken. Ratio of Na+ and K+ concentrations in shoots to roots (SNK and RNK) were determined by dividing the respective values of SNC and RNC by SKC and RKC, respectively. Sodium and potassium were determined by the atomic absorption spectrophotometer . Concentrations of sodium and potassium in shoots and roots were expressed in millimoles per gram (mM g−1).A separate second experiment was conducted to measure physiological traits related to ST, such as Na34. SNPs with minor allele frequency (MAF) less than 0.05 were culled and finally 395,553 SNPs were used for GWAS.High-density rice array (HDRA) comprised of 700 K SNPs were used for genotyping the panel. The HDRA was developed as an Affymetrix Custom Gene Chip Array from a SNP discovery dataset of about ~16 M SNPs (generated by re-sequencing 128 rice samples at ~7X genome coverage)th day after salinization was calculated and used for data analysis. Pearson’s correlations among the phenotypic traits measured at the germination and seedling stages were calculated by using SAS PROC CORR35. Analyses of variance was performed to determine significances of variation due to replications and genotypes for all measured ST traits by SAS PROC GLM35.According to seedling survival days and corresponding number of survival plants every day, weighted average of SSD at the 1636. A threshold of p-value (1.0 × 10−5) was used to claim significant SNP-trait associations and significant SNPs in <200 kb distances were considered as a single QTN38.For QTN identification, 395,553 SNPs and 208 accessions were used to detect SNP-trait associations using GWAS. Marker-trait associations were conducted by compressed mixed linear model implemented in GAPIT with the default settings except for the PCA setting as 3https://cran.r-project.org/web/packages/mrMLM/index.html) in R software and critical LOD score for significant QTN were used for the confirmation of the identified QTN26.The multi-locus GWAS analysis was performed by mrMLM package (38. The following three steps were conducted to identify candidate genes for each important QTN: (I) identify all non-synonymous SNPs in CDS of all genes located inside the important QTN region; (II) genes containing SNPs detected with −log10(p) >3; and (III) statistically significant differences detected between different major haplotypes (containing more than 8 samples) consisting of all non-synonymous SNPs within each of previous identified candidate genes within the QTN region.For selecting candidate genes in important QTN regions, QTN meeting at least one of the following criteria were considered as important: (1) close (<1 Mb) to the cloned genes or fine mapped QTL; (2) accounting for over 10% of the phenotypic variance+ and K+ concentrations in roots (RNK)  was significantly correlated with the final ST traits, SST and SSD. Significant and positive correlation was observed only between shoot Na+ concentration (SNC) and root K+ concentration (RKC) and between SST and shoot Na+/K+ ratio (SNK). Significant negative correlation was observed between SST and SSD, and between SNC and shoot K+ concentration (SKC). No correlation was observed between the ST traits measured at the germination stage and those at the seedling stage, except for a weak but significant negative correlation between SL at the germination stage and SNK at the seedling stage, indicating ST at the two developmental stages of rice were largely under independent genetic controls.Significant and positive correlation was observed between root length (RL), SL and GR at the germination stage Table . At the In total, 395,553 SNPs covering 372 Mb of the rice genome were used for genetic analysis of the population. SNPs were well distributed throughout the genome, ranking from 25,045 SNPs Table .Table 3GqSL2, qSL6, qGR4 and qRL8) were identified using GAPIT and confirmed by mrMLM while two additional QTN (qGR3 and qRL12) were detected by mrMLM. For SL, two QTN (qSL2 and qSL6) were identified on chromosomes 2 and 6 with LOD values of 6.06 and 8.08, which explained 9.6% and 9.2% of the total SL phenotypic variance, respectively. The estimated genetic effect was 0.28 for qSL2 and 0.19 for qSL6. For GR, two QTN (qGR3 and qGR4) were identified on chromosomes 3 and 4 with LOD values of 4.31 and 3.02, which accounted for 9.6 and 9.1% of the total phenotypic variance and had fairly large genetic effects of 7.69 and 8.49 in germination rate. For RL, two QTN qRL8 and qRL12 were identified on chromosomes 8 and 12, which accounted for 9.7 and 8.5% of the phenotypic variance with genetic effects of 0.23 and 0.77 in RL, respectively.In total, six QTN affecting the three traits related to rice ST at the germination stage were detected Table . Four QTIn total, 14 QTN were identified for eight seedling stage ST related traits. These QTN locate on all rice chromosomes except 3 and 7 and explained 8.9–10.8% of the trait phenotypic variances (Table qSKC9 and qSKC11) were identified on chromosomes 9 and 11 with LOD value 3.89 and 5.22 and explained 10.8% and 9.1% of the trait phenotypic variance, respectively, which had genetic effects of 10.1 and 15.3 in SKC. For RNK, one QTN (qRNK2) was identified on chromosome 2 with LOD of 6.04, explaining 10.7% phenotypic variance with a genetic effect of 0.34 in RNK. For SNK, two QTN (qSNK1 and qSNK12) were identified on chromosomes 1 and 12 with LOD value 4.99 and 5.99 and explained 10.3% and 10.1% of the trait phenotypic variance with genetic effects of −0.59 and 0.33, respectively in SNK. For SNC, two QTN, qSNC1 and qSNC6, were identified on chromosomes 1 and 6 with LOD value 4.16 and 9.01 and accounted for 10.1% and 10.4% of the phenotypic variance, respectively. For RDW, one QTN (qRDW10) was identified on chromosome 10 with LOD values of 4.41 and explained 8.9% of phenotypic variance. For SDW, two QTN (qSDW9a and qSDW9b) were identified on chromosome 9 with LOD values of 6.92 and 4.31, which accounted for 10.7% and 11.1% of phenotypic variance, respectively. For SST, three QTN  were identified on chromosomes 5, 6 and 9 with LOD values of 4.13, 6.10 and 6.88, which explained phenotypic variance of 10.4%, 9.6% and 10.7%, respectively. For SSD, one single QTN (qSSD5) was identified on chromosome 5 with a LOD value of 4.72 and explained 10.8% of phenotypic variance. Surprisingly, none of the above QTN were mapped closely one to another.For SKC, two QTN  of three QTN  identified at the germination stage. Significant (−log10(P) >3) non-synonymous SNPs were identified in the CDS region of DSM3, but not in the CDS regions of OsGMST1 and OsCCC1.With the resolution of 200 kb for all identified QTN, we were able to narrow down a relatively small number of candidate genes for each of the identified QTN. We focused on those candidate genes that locate within the 200 kb region of each identified QTN and also contain nonsynonymous SNPs in their CDS regions among the 208 rice panel. We found three cloned ST genes, qGR3, qSNK1, qSNK12, qSNC1, qSNC6, qRNK2, qSDW9a, qSST5 and qSST9) were identified based on the two criteria  were identified with −log10(P) >3. Two haplotypes were identified for each of the two candidate genes (Os12g07990 and Os12g08030) with significant phenotypic differences detected between the two haplotypes at each of the two candidates  identified with −log10(P) >3. Significant phenotypic differences were detected among four haplotypes at Os01g41930  were highly significant with −log10(P) >3. Significant phenotypic differences in SNC were detected among the three haplotypes at Os06g30390  with −log10(P) >3 as the likely candidates. We identified three haplotypes at four candidate genes  with significant phenotypic differences among them for RNK  were most likely candidate genes with −log10(P) >3. We detected significant phenotypic differences for SDW among the three haplotypes at Os09g03750  >3. We detected three haplotypes with significant difference for SST among them  associated with SL at the germination stage was adjacent to the cloned ST gene OsGMST1, which is specifically expressed under salt stress, while reduced expression of this gene is associated with hypersensitivity to salt stress in rice45. Similarly, qGR3 (6.83–7.19 Mb on chromosome 3) associated with GR at the germination was adjacent to DSM3, which is an important member of the OsITPK family. DSM3 produces stress resistance under drought and salt in rice46. qRL8 (12.50–12.70 Mb on chromosome 8) associated with RL at the germination under salinity was adjacent to the cloned ST gene, OsCCC1 (cation-Cl− cotransporter)14, which is involved in K+ and Cl− transport and had a significant role in K+ and Cl− homeostasis and rice plant development. qRNK2 in the region of 24.24–24.40 Mb on chromosome 2 was mapped in a genomic region adjacent to RSS1 that is reportedly able to maintain the vigor and viability of the meristematic cells under salinity, while inadequate functioning of RSS1 would cause an extreme dwarf and short-root phenotype under high-salt but not under the normal growth conditions47. Others included qSNK1 in the region of 11.40–11.60 Mb on chromosome 1, which affected SNK in shoots, was mapped in the genomic region adjacent to the cloned ST gene, SKC1 encoding a member of HKT-type transporters for K+ homeostasis in rice shoots13. qSST5 was mapped in the adjacent region of OsTZF1, a member of the CCCH-type zinc-finger gene family of rice whose expression induces ST and drought tolerance in rice48. qSST9 associated SST in the region of 20.61–20.79 Mb on chromosome 9 was mapped together with the cloned gene OsEATB15, which was reportedly down-regulated and associated with tillering and panicle branching under salinity. These results implied that the false positive probability would be very low for the ST QTN identified in this study.In this study, identification of many QTN and their candidate genes/alleles for ST traits of rice by GWAS should be considered more efficient when compared with most QTN mapping studies of similar scale by linkage mappingly Table . For exaOs01g20160 and Os01g20720 for qSNK1. Os01g20160 encodes an OsHKT1-5-Na+ transporter which was reportedly involved in Na+ transportation and K+ homeostasis13. Os01g20720 encodes CC-NBS-LRR protein, which is known to be able to regulate the signaling pathway to establish rice defense mechanism under stress conditions50. Similarly, the most likely candidate genes for qSNK12 included Os12g07970 and Os12g07990. The former encodes a transporter and major facilitator family protein which the latter encodes putative protein of kinase family. Both proteins are reportedly involved in plant defense and stress tolerance51 and hence are the most likely candidate genes of qSNK12. Similarly, our result suggested Os01g41930 and Os01g42040 were the most likely candidates for qSNC1. Os01g41930 encodes a leucine rich repeat protein which is up-regulated under cold and drought stress in rice52 while the result of haplotype analysis  putative protein. ANK proteins are mainly involve in specific protein-protein interaction56. For qGR3, Os03g12840 was most likely candidate gene for germination, it encodes for the production of putative inositol 1,3,4-trisphosphate 5/6-kinase and cause less accumulation of osmolytes and soluble sugar in root46. Currently, all the 22 candidate genes for rice ST are being verified by genetic transformation and further molecular analyses.Another major advantage in our QTN mapping by GWAS was the high resolution for the identified QTN. In this study, we used 395,553 SNPs in our genotyping and for QTN identification, which allowed us to narrow down many identified ST QTN each to a small genomic region <200 kb and shortlist candidate genes to a small number of genes for each of the identified QTN. Further, SNPs in CDS regions within each identified candidate genes were used for haplotype analyses for conforming the identified candidate genes, which allowed us to further shortlist very few or even a single candidate gene for some of the ST QTN. Using this strategy, we were able to shortlist 22 candidate genes for eight ST QTN identified in this experiment. These included two candidate genes, 57, our results demonstrated several advantages of GWAS such as high genetic diversity and high mapping resolution. We also, however, noted a few limitations of this approach. These included poor ability to detect rare QTN/QTL alleles and QTN of small effect and inability to detect epistasis. During our analyses, we tentatively removed the minor alleles to minimize the false positive probability, thus QTN associated with the unique or rare alleles were undetectable in this study. We also realized that in our haplotype analyses, uses of non-synonymous SNPs in gene CDS regions could only capture part of the phenotypic variation associated by those mutations, but unable to detect those mutations occurring in the gene promoter regions that are known to be able to change gene expression and cause trait variation. Because SNPs in the promoter regions of the candidate genes were not covered in our haplotype analyses, some of the QTN candidate genes could have been incorrectly predicted or missed. The most likely examples in this study included qSL2 and qRL8 for which we were not able to identify any significant non-synonymous SNPs in their QTN confidence intervals. An additional problem for the accuracy in identifying QTN and candidate genes by GWAS is expected to be affected to a certain degree of the gene presence and absence variation when a single reference genome is used in SNP calling and candidate gene prediction, because it is already known that a significant level of gene presence and absence variation exists in rice germplasm58. Fortunately, this problem can be largely overcome when more and more new reference genomes are publicly available59. Finally, with so many ST QTN and their candidate genes identified and the availability of high density SNP markers, it remains a big challenge to pyramid many ST QTN/genes for improving rice ST in breeding, even with the current genome selection technology61. The good news is that strong phenotypic selection under appropriate salt stress is able to pyramid and quickly fix large numbers of ST loci in very few generations62, even though this phenomenon remains poorly understood genetically and at the molecular level.Consistent with previous reportsSKC1 encoding a member of HKT-type transporters for K+ homeostasis, OsTZF1 (a member of the CCCH-type zinc-finger gene family) for ST and drought tolerance in rice and OsEATB associated with tillering and panicle branching under salinity. A total of 22 candidate genes and important ST alleles were identified for nine important ST QTN based on combined bioinformatics and haplotype analyses. The results provided useful germplasm and genetic information for future improvement of ST in rice.Tremendous amounts of genetic diversity for 13 ST-related traits existed in rice germplasm. Using GWAS, 6 and 14 QTN were identified for ST-related traits at the germination and seedling stages, respectively, several of which were mapped to the genomic regions of previously cloned ST genes, including Supplementary Table S1, Supplementary Table S2, Supplementary Table S2, Supplementary Figure S1


Myopia, or near-sightedness, is our most common eye condition and the prevalence is increasing globally. Visual impairment will occur if uncorrected, whilst high myopia causes sight-threatening complications. Myopia is associated with higher intelligence. As both are heritable, we set out to examine whether there is a genetic correlation between myopia and intelligence in over 1,500 subjects (aged 14–18 years) from a twin birth cohort. The phenotypic correlation between refractive error and intelligence was −0.116 (p < 0.01) - the inverse correlation due to the fact that myopia is a negative refractive error. Bivariate twin modeling confirmed both traits were heritable  and the genetic correlation was −0.143 (95% CI −0.013 to −0.273). Of the small phenotypic correlation the majority (78%) was explained by genetic factors. Polygenic risk scores were constructed based on common genetic variants identified in previous genome-wide association studies of refractive error and intelligence. Genetic variants for intelligence and refractive error explain some of the reciprocal variance, suggesting genetic pleiotropy; in the best-fit model the polygenic score for intelligence explained 0.99% (p = 0.008) of refractive error variance. These novel findings indicate shared genetic factors contribute significantly to the covariance between myopia and intelligence. Myopia, or near-sightedness, occurs when a viewed object is focused in front of the retina resulting in the observer seeing a blurred image. This generally occurs a result of axial elongation, or lengthening, of the eyeball during childhood. Refractive correction in the form of glasses, contact lenses or refractive surgery is required in order for a clear image to be obtained. It is the most common ocular condition and the prevalence is increasing globally, most dramatically in urban East Asia123Environmental factors are known to play a key role in myopia risk. There are well-established links between myopia and urbanization, lack of time outdoors, reduced light exposure, socio-economic status, prenatal factors, near work, and educational attainment5678910113131415171819202122231518However, the nature of the association between myopia and IQ remains poorly understood. While it may reflect inadequate adjustment for reading/time outdoors, one potential explanation is that myopic children, with their cumbersome glasses, may be less likely to play sports outdoors and more likely to spend time on their school studies283033The twin model provides the ‘perfect’ natural experiment to examine the relative effect of genes and environment on trait variation. The technique allows global estimation of genetic and environmental effects regardless of underlying genes or specific environmental factors36Data on refractive error and IQ were available for 1529 twin subjects, summarized in The phenotypic correlation between refractive error and IQ, adjusted for the effects of age and sex, was −0.116 (p < 0.01)  - the neBivariate twin modeling estimated the heritability of refractive error at 85% (95% CI 79.9–87.5) and at 47% (95% CI 36.7–57.8) for IQ . Shared rA), that is the correlation between the genetic influences on refractive error and the genetic influences on intelligence, was −0.143 (95% CI −0.013 to −0.273). Shared genetic effects can be estimated as follows: √A(Refractive Error) x rA x √A(IQ). This gives an estimate of 0.091. Therefore, it can be calculated that the proportion of phenotypic correlation between refractive error and IQ due to shared genetic effects is 78%.The genetic correlation (Polygenic risk scores (PRS) can be used to estimate the degree of phenotypic variance explained by the contribution of thousands of common genetic variants (SNPs) previously associated with the trait of interest or, in this analysis, an alternate trait. PRS for childhood IQ were calculated for all unrelated individuals in TEDS with genome-wide association data using eight thresholds of significance for inclusion of variants (see Methods) from the results of a GWAS for child IQ, excluding TEDSSimilarly, a polygenic risk score for refractive error was calculated on all genotyped participants using eight thresholds of significance from the results of a GWAS for refractive error in adultsTwin participants with high IQ (highest quartile) were one and a half times more likely to be myopic, comparable to others18et al. reported that 76% of the phenotypic sharing between refractive error and educational attainment was due to shared genetic factorsTo our knowledge no previous study has examined the extent of shared genetic factors for myopia and IQ. Previous bivariate twin analyses for myopia have examined the relationship with axial length and with educational attainment36The argument that highly intelligent children, who may spend more time on near-work activities, increase their risk of developing myopia has long been favored89404228452829In axial myopia, the commonest form of myopia, elongation of the eye results in a focused image falling in front of the retinal plane. The retina, together with a number of other ocular structures, including the ciliary body which controls accommodation (near focus), originate embryonically from the same tissue as the brain (neuroectoderm)5153Globally, myopia is becoming more common and IQ scores are rising159This analysis utilizes a powerful twin data set with phenotypic and molecular genetic data; for the IQ PRS comprising of SNPs over a significance threshold of 0.1, we have enough statistical power to detect a genetic covariance of 0.09 between IQ and refractive error64In summary, our bivariate twin model suggests that shared genetic factors underlie the majority of the phenotypic correlation between myopia and IQ. This was substantiated using molecular genetic data where approximately 1% of refractive error variance was explained by genetic variants linked to IQ. This provides novel evidence for a modest but significant contribution of pleiotropic genetic factors contributing to the development of myopia and higher intelligence.The Twins Early Development study (TEDS) is a longitudinal birth cohort of twins studied from a neurodevelopmental perspective using multivariate quantitative and molecular genetic techniques. In the initial TEDS study over 15,000 families of twins born in England and Wales in 1994, 1995 and 1996 were recruited. The sample remains representative of the UK populationPostal questionnaires were sent to 2625 families inviting participation in the myopia study and consent was requested from the parents, as well from the twins, to contact their optician for a recent refraction. A response rate of 51.7% of potential twin participants was achieved (n = 2715). Responders and non-responders were comparable in terms of ethnicity, gender, zygosity, and parental employment; however there was a slightly higher rate of twin and parental secondary school examinations achievement in the responders. Study questionnaires were sent to the optometrists given by 2,283 twins, from whom informed consent was obtained, requesting a brief ophthalmic and refractive history together with a most recent refraction. Non-cycloplegic subjective refractive error measurements were obtained for 1996 individuals . Spherical equivalent (SE) was calculated using the standard formula (SE = sphere + (cylinder/2)) and the mean of the two eyes was considered for each individual. Myopia was defined as SE ≤ −0.75 diopters (D). Standardized residuals of mean spherical equivalent adjusted for age and sex were calculated (n = 1991).Multiple child and parent questionnaires, in addition to teacher questionnaires, web-based testing and home assessments, have been conducted over the twins’ life-course. General cognitive ability or g6869Genotyping was performed on 3665 individuals (one twin per pair) on Affymetrix GeneChip 6.0 single nucleotide polymorphisms (SNP) genotyping arrays  using standard experimental protocols, as part of the WTCC2 project. Twins excluded from genotyping were children with serious medical or perinatal problems, non-white ethnic origin, and English spoken as a second language at home.” A total of 3152 DNA samples  survived quality control for relatedness, hetereozygosity, ancestry and hybridization intensity outliers. Genotypes at untyped markers were imputed with HapMap phase II and III, and WTCCC2 controls using IMPUTE (v2). The quality control criteria used to select imputed SNPs were an information score of ≥0.90 for WTCCC2 controls and ≥0.98 for HapMap imputation. Zygosity was assigned using parental questionnaires of physical similarity; this has shown over 95% accuracy when compared to DNA testing2 or coefficient of determination) for refractive error with IQ was observed in univariate and multiple linear regression models, adjusting for some of the known risk factors for myopia with refractive error considered as a continuous trait and myopia as a binary trait (≤−0.75 D). The association between different quartiles of IQ and also non-verbal and verbal IQ were evaluated. In analyses p < 0.05 was considered statistically significant.Correlation coefficients between refractive error and IQ, adjusted for age and sex, were calculated. The association and variance explained (rhttp://openmx.psyc.virginia.edu) in R (http://www.R-project.org). Heritability (or h2) is provided by the estimate for additive genetic effects. A bivariate Cholesky decomposition model for IQ and refractive error was constructed to assess the phenotypic variance and covariance attributable to genetic and environmental factors. There are two mathematically equivalent solutions to the bivariate model and for this analysis we selected the correlated factors solution which does not assume that the factors underlying the first variable influence the second variable and allows ascertainment of the proportion of phenotypic correlation due to A, C & E. Age and sex adjusted standardized residuals were used for both traits. The degree of phenotypic correlation explained by genetic factors was calculated by dividing the estimate of the shared genetic effects by the phenotypic correlation.In twin modeling the phenotypic variance of a trait is partitioned into three factors: additive genetic effects (A), non-additive genetic effects (D) or the shared environment between siblings (C), and the individual-specific environment effects (E). Monozygotic pairs (MZ) have the same genetic and shared environmental effects, whereas in dizygotic twins (DZ) additive genetic effects are 50% correlated, but the shared environmental effects are the same. An ACE model, rather than an ADE model, was chosen based on the twin correlations for the traits and in an effort to examine any potential differences in shared and unique environmental effects on the traits. We performed standard ACE model-fitting analysis using the OpenMx package , and then vice versa in 1517 individuals. In each model the significance of the PRS  and variance explained (assessed by r2) was observed. Analysis was performed using Plink v1.9Polygenic risk scores (PRS) enable estimation en masse of the genetic contribution of thousands of common variants, generally of small individual effects, on the variation of a trait. In this study, estimation, at a participant level, of the degree of variance of one trait (eg refractive error) explained by the SNPs associated with a second trait (eg. IQ) from an unrelated sample was examined. The results from a large international meta-analysis GWAS for IQHow to cite this article: Williams, K. M. et al. Phenotypic and genotypic correlation between myopia and intelligence. Sci. Rep.7, 45977; doi: 10.1038/srep45977 (2017).Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.


Studying the consequences of addictive behaviours is challenging, with understanding causal relationships from observational data being particularly difficult. For example, people who smoke or drink excessively are often systematically different from those who do not, are less likely to participate in research and may misreport their behaviours when they do. Furthermore, the direction of causation between an addictive behaviour and outcome may be unclear. Mendelian randomization (MR) offers potential solutions to these problems.We describe MR's principles and the criteria under which it is valid. We identify challenges and potential solutions in its application (illustrated using two applied examples) and describe methodological extensions in its application.ADH1B gene) and cardiovascular risk has been investigated, finding that alcohol consumption increases risk, with no evidence of a cardioprotective effect at moderate consumption levels. In addition, heaviness of smoking (proxied by a variant in the CHRNA5‐A3‐B4 gene cluster) and risk of depression and schizophrenia have been investigated, with no evidence of a causal effect of smoking on depression but some evidence of a causal effect on schizophrenia.MR is subject to certain assumptions, and requires the availability of appropriate genetic data, large sample sizes and careful design and conduct. However, it has already been applied successfully to the addiction literature. The relationship between alcohol consumption (proxied by a variant in the Mendelian randomization analyses are already producing robust evidence for addiction‐related practice and policy. As genetic variants associated with addictive behaviours are identified, the potential for Mendelian randomization analyses will grow. Methodological developments are also increasing its applicability. Determining whether associations are causal is central to much addiction research but is challenging, with many observational associations unlikely to reflect causal relationships Mendelian randomization (MR) provides a tool for assessing the causal effects of behaviours on outcomes, although only when genetic variants associated with behaviours are known Traditional observational studies face three major threats to establishing whether or not an association is causal First, characteristics of people with addictive behaviours (e.g. those who smoke or drink excessively) may differ systematically from other people. In naive comparisons of exposed and unexposed groups, these confounding factors are often responsible for observed differences in outcomes. Theoretically, if all confounding factors were measured and accounted for perfectly, an observational study could establish the effect of a behaviour accurately (provided other biases did not exist) Secondly, it can be difficult to establish the direction of causation (i.e. whether reverse causation exists). While longitudinal studies may help , this is not always the case; the timing of the outcome in relation to behaviour may be uncertain. For example, when examining alcohol consumption and heart disease (Box 2) it is possible that behaviour change occurred before the early stages of disease were detected and diagnosed.Thirdly, collider bias may occur, whereby stratification on a common effect can result in a spurious correlation between otherwise independent variables In MR, genetic variants are used as proxies for the exposure of interest, which helps to avoid some of the problems described above. MR is an example of instrumental variable (IV) analysis that has long been used by economists to study causal effects The genetic variant must be associated with the exposure of interest (i.e. the behaviour being studied),The genetic variant must be independent of any confounders of the exposure–outcome relationship being studied; andThe genetic variant should only affect the outcome through the exposure of interest.In MR, genetic variants can be used as IVs to either assess whether a causal effect between exposure and outcome exists at all, or to measure the magnitude of the causal effect of the exposure on the outcome. Box 1 provides an overview of the principles for conducting a MR analysis. For a genetic variant to be a valid IV, it must satisfy three conditions:Define the research question, objectives and protocol: define exposure(s) and outcome(s), data analysis methods, variables to be used, statistical power calculations Identify data source(s): identify potential data sources  for the association between the genetic variant and the exposure, and for the association between the genetic variant and outcome. Two‐sample MR (see below) requires data for both associations to come from the different sources (see Estimate the gene–exposure association: (i.e. test condition 1) for example, by regression of the exposure variable on the effect allele (or genetic risk score if multiple genetic variants are in use). If possible, calculate a partial F‐statistic, which provides an indication of the strength of the genetic instrument Estimate associations between the genetic variant and measured confounders:  again, this might take the form of regression of measured confounders on the effect allele or genetic risk score. If multiple study populations are in use, do this for all populations where data on measured confounders are available.Estimate the gene–outcome association: for example, by regression of the outcome on the effect allele or genetic risk score, this is often referred to as the ‘reduced form’ Estimate the magnitude of the causal effect: this step is not necessary if the researcher is interested only in whether a causal effect exists, but if there is interest in the magnitude of effect this can be estimated as the ratio of the gene–outcome (reduced form) to the association between the exposure (or behaviour) and the genetic variant. Alternatively, one can first estimate the relationship between the genetic variant and the behaviour—for example, using conventional regression methods—and then estimate the relationship between the predicted behaviour from the first regression model and the outcome. In practice, rather than estimating two separate models, a jointly estimated two‐stage regression model may be used to take account of uncertainty in the predicted values from the first stage. It is worth noting that the magnitude of the causal effect should not be calculated for certain genetic instruments  Assess the plausibility of assumptions: consider whether in the study setting the results could have been affected by pleiotropy, canalization, population stratification or unmeasured confounding . These issues should at least be discussed in reporting results or where possible, formally tested.The following is intended as a general guide to the principal stages of an MR analysis, acknowledging that this (and particularly step 7) may evolve as newer techniques emerge. Interested readers may wish to consider three other reviews These conditions are illustrated graphically in Fig. CHRNA5‐A3‐B4 nicotinic receptor subunit gene cluster is associated with the heaviness of smoking in smokers, rather than smoking uptake per se (see Box 2 for an example using this variant for MR). It is therefore important to consider what specific aspect of behaviour the genetic variant reflects when interpreting MR results.Figure Define the research question, objectives and protocol: prevalence of smoking is higher among individuals with psychiatric disease  than in the general population, and individuals with these conditions tend to smoke more heavily CHRNA5‐A3‐B4 cluster of nicotinic receptor subunit genes is associated with increased smoking heaviness (number of cigarettes smoked per day) among smokers, so was considered a potential instrumental variable. Associations were estimated using traditional regression.Identify data source: individual‐level data from 63 296 participants in the Copenhagen General Population Study (CPGS).Estimate the gene–exposure association: in the CPGS study, ever smokers with 0.1 and 2 risk (T) alleles smoked an average of 13.6, 14.5 and 15.6 cigarettes per day, respectively .Estimate associations between the genetic variant and measured confounders: there was no clear evidence that the rs1051730 risk variant was associated with age, sex, education, marital status, income, alcohol consumption or physical activity.Estimate the gene–outcome association: among ever smokers, the smoking heaviness increasing (T) allele of rs1051730 was associated with increased odds of antipsychotic medication use [odds ratio (OR) for TT homozygote compared to CC homozygote: 1.16  = 1.02–1.31]. Due to the nature of the allele used for the MR analysis, it is not possible to estimate a useful causal effect estimate for the number of cigarettes per day on the outcome. A similar trend was observed for schizophrenia diagnoses, although statistical evidence for this association was weak. There was little evidence that this variant was associated with depression or antidepressant medication use among ever smokers.Assess the plausibility of assumptions: the rs1051730 variant is associated closely with the CHRNA5 nicotinic receptor subunit gene, which has been shown to alter response to nicotine and subsequently affects how much tobacco is consumed among smokers. Therefore, there is a plausible biological mechanism linking this variant with smoking behaviour. It is believed not to influence the likelihood of someone becoming a smoker in the first place  of a causal effect. As noted earlier, condition 3 (the exclusion restriction) requires no causal pathway between the genetic variant and the outcome, except through the exposure of interest. In MR studies, pleiotropy can violate this assumption Finally, cautious interpretation is necessary, bearing in mind the nature of the causal effect being estimated. For example, the study in Box 3 provides an estimate of the effect of the rs1229984 genetic variant on heart disease, indicating a causal effect of alcohol consumption. However, this genetic variant was associated both with units of alcohol consumed per week and with binge drinking. Attempts to estimate the magnitude of causal effects for specific drinking behaviour patterns, such as units per week, or binge drinking would be biased due to violation of condition 3 (as the genetic variant affects both behaviour patterns). Even when a genetic variant meets the three conditions to be a valid instrument, it may not provide an unbiased estimate of the effect of the specific aspect of behaviour that is of interest or has been measured Define the research question, objectives and protocol: observational studies often report a J‐shaped association between alcohol and cardiovascular outcomes such as coronary heart disease ADH1B) has been identified in previous research as being associated with lower alcohol consumption and so was identified as a potential genetic instrument. Associations were estimated with standard regression techniques in multiple studies and then pooled using meta‐analysis.Identify data sources: individual participant data on 261 991 participants of European ancestry were gathered from across 56 genetic studies.Estimate the gene–exposure association: carriers of the risk allele at rs1229984 consumed fewer units of alcohol per week , had lower odds of heavy drinking  or binge drinking  and higher odds of abstention  compared to non‐carriers.Estimate associations between the genetic variant and measured confounders: the rs1229984 risk variant was not associated with physical activity or with most measures of smoking, although it was associated with slightly higher odds of ever smoking , which is in the opposite direction to observational studies, and with slightly more years of education .Estimate the gene–outcome association: the rs1229984 risk variant was associated with reduced odds of heart disease among the whole sample  and among drinkers , suggesting that lower consumption is protective. Associations of the risk allele with heart disease did not differ further across light, moderate and heavy drinkers. This is contrary to the increased risk that would have been expected among light/moderate drinkers if moderate alcohol consumption had a true, causal protective effect relative to very low consumption. This suggests a linear, rather than a J‐shaped relationship between alcohol consumption and heart disease.Assess the plausibility of assumptions: the ADH1B gene is involved in metabolizing alcohol, with the rs1229984 risk variant increasing the likelihood of unpleasant symptoms after consumption. Thus, there is a plausible biological mechanism connecting the genetic variant to alcohol consumption. The weak associations between the genetic variant and measured confounders are unlikely to explain any association between the genetic variant and heart disease, but it is possible that unmeasured confounders could be biasing results if transmission of the genetic variant across generations is related to alcohol consumption (i.e. assortative mating is occurring). Among non‐drinkers the rs1229984 risk variant was not associated with heart disease , suggesting that it has no effect other than via reductions in alcohol consumption. This estimate may have been affected by collider bias because the genetic variant is associated with both abstention and heaviness of drinking among drinkers  threaten the validity of MR. While there remain no definitive ways of addressing this, several approaches now exist to explore potential bias. A theory‐informed approach is to make potentially informative comparisons to check the plausibility of assumption 3. For example, looking throughout countries with differing cultural norms for alcohol consumption can help to establish whether biological pleiotropy exists. In East Asian countries women tend not to consume alcohol, so genetic variants related to alcohol consumption would be expected to be associated with alcohol‐related disease outcomes in men but not in women Newly developed methods allow empirical investigation of MR assumptions. The funnel plot is used to identify small study bias in systematic reviews by looking for an association between study precision and effect size Analytical tools for MR research are developing and being refined rapidly. Bidirectional MR is an extension of the traditional design utilizing genetic markers for different but inter‐related outcomes to investigate the direction and magnitude of the causal effects. For example, the causal relationship between cannabis use and schizophrenia remains controversial. Gage and colleagues studied two sets of genetic variants, one related to cannabis initiation and one related to schizophrenia risk, to understand more clearly the direction of causation Finally, factorial MR allows combinations of multiple behaviours to be investigated. Factorial MR is akin to a factorial RCT where the population is in effect allocated randomly to receive any combination of the behaviours under consideration MR adds to the range of study designs available to understand the causal effects of behaviours on outcomes of interest. It helps address key limitations of traditional observational studies, including confounding and reverse causation, but selection bias could remain problematic. MR studies potentially allow researchers to produce more robust evidence on questions of immense relevance to policy and practice. They can provide strong evidence of causation, subject to necessary assumptions which benefit from an understanding of the underpinning biological processes. However, two of the three assumptions underpinning MR cannot be tested definitively. Furthermore, genetic variants known to be associated with behaviours of interest are required and genetic data from a large number of people, including those exhibiting the behaviour of interest, are needed. A range of other causal approaches to observational research are available, with differing underpinning assumptions; their use in combination can be particularly powerful None.


P < 0.001) were identified for nine yield-related traits on chromosomes 1A, 1D, 2A (2), 3B, 4A (2), 4B, 5A (4), 5B (4), 5D, 6B (2), 7A (2), and 7B (3), explaining 10.86–20.27% of the phenotypic variations. Of these, four major loci were identified in more than three environments, including one locus for RLW (6B), one locus for TKW (7A), and two loci for PH (7B). A cleaved amplified polymorphic sequence (CAPS) marker Td99211 for TKW on chromosome 5A was developed and validated in both a natural population composed of 372 wheat varieties (lines) and a RIL population derived from the cross of Yangxiaomai × Zhongyou 9507. The CAPS marker developed can be directly used for marker-assisted selection in wheat breeding, and the major MTAs identified can provide useful information for fine-mapping of the target genes in future studies.Genetic improvement of grain yield is always an important objective in wheat breeding. Here, a genome-wide association study was conducted to parse the complex genetic composition of yield-related traits of 105 elite wheat varieties (lines) using the Wheat 90K Illumina iSelect SNP array. Nine yield-related traits, including maximum number of shoots per square meter (MSN), effective number of spikes per square meter (ESN), percentage of effective spike (PES), number of kernels per spike (KPS), thousand-kernel weight (TKW), the ratio of kernel length/kernel width (RLW), leaf-area index (LAI), plant height (PH), and grain yield (GY), were evaluated across four environments. Twenty four highly significant marker-trait associations (MTAs) ( Triticum aestivum L.) is one of the most important and widely-grown staple crops. The continuous decrease in farmland and rapid increase in population results in big problems regarding the production of sufficient food to meet the global demand. A previous study examining food security suggested that food production would need to increase by 70–100% in 2050   –27. The ™ Homogenizer  for genomic DNA extraction following the MPure Nucleic Acid Purification system . The DNA quality was checked by 1.0% agarose gel electrophoresis, and the concentration was determined with the NanoDrop ND-200 Nanophotometer .Dry seeds were ground to powder using the FastPrep-96https://www.illumina.com/). The accuracy of the SNP clustering was visually validated, and incorrectly clustered SNPs were manually adjusted. The SNP markers with a missing rate exceeding 0.1 or a minor allele frequency less than 0.05 were removed, and 31,250 effective SNPs were used for subsequent population structure, principal component, and kinship analyses. Of these, 15,430 SNP markers mapped on different chromosome regions based on the genetic and physical maps [Samples were genotyped using the wheat 90K Illumina iSelect array containing 81,587 SNP markers at Beijing Compass Biotechnology Co., Ltd., following the manufacturer’s protocol , in whiccal maps  (S1 Tablhttp://rajanil.github.io/fastStructure/). Multiple K values ranging from 1 to 10 were implemented using the Simple Model prior to obtaining a reasonable range of values for the appropriate model complexity required to explain the population structure [K [Q matrix was obtained based on a variation inference executed for a choice of K, and the ancestry contribution of each model component was computed as the mean admixture proportion for all samples [The population structure of the association mapping panel was assessed with all 31,250 effective SNP markers on 21 wheat chromosomes, using the fastStructure algorithm in Python  was conducted with numerical values for genotypes  using the genome association and prediction integrated tool (GAPIT) of the R software . A turniK*) was calculated with the same genotypes using the VanRaden method, and then used to create a clustering heat map of the association mapping panel in the GAPIT [The marker-based kinship matrix (he GAPIT .Q matrix as the fixed effect and a kinship matrix as the random effect (Q + K*) [K*), at a threshold of P < 0.001. Because the degree of the correlation with different models varied from trait to trait, a Bayesian information criterion (BIC)-based model comparison was used for each phenotype [n)·number of estimated parameters (n = sample size). The model with Q + K* or PCA + K* as covariates was selected for each trait according to the maximum BIC value [P < 0.001) was assumed as a major locus.A GWAS was performed using the mixed linear models in TASSEL (version 5.2) –34. The (Q + K*)  as well henotype . The criIC value –38. The Tdurum_contig71499_211) on chromosome 5A significantly associated with TKW (P < 0.001), a CAPS marker was developed, designated Td99211 , using Primer premier 5.0. PCR was performed in a total volume of 10 μL, including 1.0 μL of 10 × PCR buffer, 200 μM of dNTPs, 4 pmol of each primer, 0.5 U Taq DNA polymerase and 100 ng of template DNA. The PCR procedure included a denaturation at 94°C for 5 min, followed by 38 cycles of denaturation at 94°C for 30 s, 60°C for 30 s, 72 `C for 30 s, and a final extension at 72°C for 8 min. The PCR products were digested with AluI at 37°C for 3 h  according to the manufacturer’s directions, and separated on 1.5% agarose gel. The SPSS Statistics 20 software was used for data analysis, and t-tests were performed using the independent-samples t-test.Based on a SNP  to 0.92 (PH). Among three major yield components, TKW (0.88) had the highest HB2, followed by KPS (0.75), and ESN (0.64).The phenotype values of GY and related traits  of the association panel in different environments were shown in t traits . The HB2The BLUPs for GY and related traits were positively correlated with the measured data in different environments (0.61–0.97) . There wQ matrix (K = 4) and kinship matrix (K*) as well as a PC matrix (PC8) and kinship matrix (K*) were used as the covariates for a subsequent association study. The panel of 105 wheat varieties and advanced lines was divided into four subpopulations based on model complexity. The 105 elite breeding varieties were assigned to each subpopulation according to ancestry contributions  were detected on chromosomes 1A, 1D, 2A (2), 3B, 4A (2), 4B, 5A (4), 5B (4), 5D, 6B (2), 7A (2), and 7B (3) using the Q + K* or PC8 + K* models for these traits. These MTAs could explain 10.86–20.27% of the phenotypic variance , 3B , 4A , and 4B , explaining 12.18–16.01% of the phenotypic variance. However, all SNPs related to ESN were only detected in one environment or not (P < 0.001), suggesting the genetic instability of these MTAs in different environments.Four MTAs for ESN were identified on chromosomes 1D  on chromosome 7A (130.27 cM), explaining 11.78–12.45% of the phenotypic variance.For KPS, we detected only one MTA  on chromosome 5A (84.13–86.36 cM), accounting for an average phenotypic variation of 12.62%. Another one with two SNPs  significantly associated in three environments  (P < 0.001) on chromosome 7A (156.23 cM), explained 13.91% of the TKW variation, which implied this MTA is a major one.For TKW, one MTA harbored three SNP markers , 5B , 6B , and 7B . Of them, the MTA on 6B was more stable and significant (P < 0.001) in four environments , explaining a higher phenotypic variance (17.68%), which implied this region covered a credible QTL.Four MTAs were identified for RLW on chromosomes 5A , 5D , 6B , and 7B  explained 13.74–20.27% of the phenotypic variance. Of them, both two MTAs on 7B (77.13 cM and 129.77 cM) were identified in three environments, indicating two independent major loci on 7B. Of these associated SNPs, wsnp_Ex_rep_c68762_67626384 on 7B was more significantly associated with PH, suggesting the importance of this region.Five MTAs for PH on chromosomes 5B  to 15.91% (wsnp_BQ166999B_Ta_2_1), and an average of 13.86%. Similar to ESN, all MTAs for GY showed a poor genetic stability in different environments.Four MTAs associated with GY were identified on chromosomes 2A, 5A, 5B, and 6B, respectively, with phenotypic contributions ranging from 11.50% (Tdurum_contig71499_211) on chromosome 5A for TKW was developed into the CAPS marker (Td99211), and genotyped in 372 wheat varieties (lines) and 188 lines from the RIL population of Yangxiaomai × Zhongyou 9507 cross. Two allelic variations were detected, designated Td99211-A and Td99211-G (P < 0.01), and the varieties (lines) harboring Td99211-G had a higher TKW compared with those carrying Td99211-A , followed by TKW (0.88) and RLW (0.85), while the LAI was the lowest (0.43). The difference of heritability is consistent with GWAS results, that is, only one SNP for LAI was detected, while four major MTAs for PH (2), TKW (1), and RLW (1) were stably identified across environments.In addition, we also analyzed the Because of the limitations of the Structure  and AdmiQ + K* model for all traits probably results in an over-correction of the population structure and some false-negative results [Q + K* and PC8 + K* models.The use of different models is suitable for studying different traits, but blindly using the  results , 32, 36.Ex_c24031_300) significantly associated with RLW was detected on chromosome 5B (212.43 cM). Chen et al. [IACX2594) for RLW in the same genetic position (212.43 cM) using a high-density Illumina iSelect 90K single nucleotide polymorphism assay in a Chinese winter wheat population. For GY, we identified a MTA (RAC875_c2926_371 and wsnp_Ku_c7890_13513783) on chromosome 5A, which was only 3.62 cM from the QTL (wsnp_Ex_c31830_40573624 and wsnp_Ex_rep_c69526_68472665) for GY reported by Li et al. [Excalibur_c14451_1313 and Kukri_c19251_579) for TKW on chromosome 7A (156.23 cM), which was adjacent to the QTLs  controlling TKW reported by Li et al. [Kukri_c9285_762) was detected on chromosome 5D in this study, which was close to BS00089597_51 (known as GA20ox1 in rice) associated with PH reported by Zanke et al. [Based on 90K-derived genetic map described by Wang et al.  S6 Tabl, we furtn et al.  also ideosome 7A 6.23 cM, osome 7A 6.23 cM, Kukri_rep_c106092_300, 113.67 cM) and GY , indicating the importance of PH to GY. However, several MTAs for different traits were detected in the same or neighboring positions as those identified in previous studies. For example, wsnp_Ex_c24376_33618864 for RLW on chromosome 7B (52.18 cM) was also identified for PH by Zanke et al. [Wsnp_Ex_c11003_17857272 for PH on chromosome 7B (77.13 cM) was detected for TKW  [Wsnp_Ex_c15944_24350833 and Excalibur_c15944_70 for ESN on chromosome 2A were located in the same position (62.57 cM) as Kukri_c21467_571 for TKW [wsnp_JD_c8158_9193784 for KW [Kukri_c48750_1372 (61.89 cM) for chlorophyll content  during grain filling [Tdurum_contig14046_364 for RLW on chromosome 6B was only 0.84 cM from the QTLs for the number of spikes per square meter  [RAC875_c31299_1215 for GY on chromosome 6B was located only 0.59 cM from the QTLs for TKW  [RAC875_rep_c71463_98) for PH [We detected a MTA on chromosome 6B with PH (Tdurum_contig71499_211) on chromosome 5A was identified to be significantly associated with TKW based on BLUP values, and a CAPS marker (Td99211) for the SNP was successfully developed. Using 372 wheat varieties (lines) and 188 lines from the RIL population of Yangxiaomai × Zhongyou 9507 cross, we further validated the association of the CAPS marker with TKW. Moreover, the Td99211-G allele was associated with higher TKW compared with Td99211-A, and thus considered as a favorable allele. Notably, only 49 (13.17%) harbored the Td99211-G allele in 372 wheat varieties (lines), indicating the Td99211-G allele have not been widely utilized in genetic improvement of wheat yield. By contrast, the favorable variations of several genes controlling TKW, such as TaGW2 [TaCWI [TaGS-D1 [TaGASR7-A1 [The SNP Click here for additional data file.S2 Table(XLSX)Click here for additional data file.S3 Table(XLSX)Click here for additional data file.S4 Table(XLSX)Click here for additional data file.S5 Table(XLSX)Click here for additional data file.S6 Table(XLSX)Click here for additional data file.S1 Fig(TIF)Click here for additional data file.S2 Fig(TIF)Click here for additional data file.


Multi-marker methods, which fit all markers simultaneously, were originally tailored for genomic selection purposes, but have proven to be useful also in association analyses, especially the so-called BayesC Bayesian methods. In a recent study, BayesD extended BayesC towards accounting for dominance effects and improved prediction accuracy and persistence in genomic selection. The current study investigated the power and precision of BayesC and BayesD in genome-wide association studies by means of stochastic simulations and applied these methods to a dairy cattle dataset.The simulation protocol was designed to mimic the genetic architecture of quantitative traits as realistically as possible. Special emphasis was put on the joint distribution of the additive and dominance effects of causative mutations. Additive marker effects were estimated by BayesC and additive and dominance effects by BayesD. The dependencies between additive and dominance effects were modelled in BayesD by choosing appropriate priors. A sliding-window approach was used. For each window, the R. Fernando window posterior probability of association was calculated and this was used for inference purpose. The power to map segregating causal effects and the mapping precision were assessed for various marker densities up to full sequence information and various window sizes.Power to map a QTL increased with higher marker densities and larger window sizes. This held true for both methods. Method BayesD had improved power compared to BayesC. The increase in power was between −2 and 8% for causative genes that explained more than 2.5% of the genetic variance. In addition, inspection of the estimates of genomic window dominance variance allowed for inference about the magnitude of dominance at significant associations, which remains hidden in BayesC analysis. Mapping precision was not substantially improved by BayesD.BayesD improved power, but precision only slightly. Application of BayesD needs large datasets with genotypes and own performance records as phenotypes. Given the current efforts to establish cow reference populations in dairy cattle genomic selection schemes, such datasets are expected to be soon available, which will enable the application of BayesD for association mapping and genomic prediction purposes. With the advent of dense single nucleotide polymorphisms (SNP) panels, it has become possible to exploit linkage disequilibrium (LD) between SNPs and genes that are involved in complex or quantitative trait variation, with the aim to map genes that underlie trait variation and to predict genomic values . Genome-In Bayesian analysis, inference on unknowns is drawn from their posterior distributions. Recently, Fernando and Garrick  and FernTo the best of our knowledge, the Bayesian models mentioned above consider only additive gene effects. However, dominance is a non-negligible source of complex trait variation –13. BoloVerbyla et al. , 17 prop−8/bp/meiosis. In total, 1051 generations were generated. For the first 650 generations, the effective population size was Ne = 600, and then decreased to 100 in the following 350 generations, with a fast decline in the last generations. This decline was chosen in order to create an LD pattern as observed in bovine populations [A forward simulation approach was used to generate a Fisher-Wright diploid population with a genome that consisted of one chromosome that was 1 Morgan (M) long. The mutation rate was 10ulations . From geulations , a simululations . In our For each population, five traits were simulated as follows. In the last generation, 15 of the 7k SNPs with a MAF higher than 0.05 were randomly selected as causal mutations. The minimum distance between two quantitative trait loci (QTL) was 2 cM. The additive effect , and hence, it mimics a situation where the full sequence is known and the causative mutations are among the full set of SNPs.The three BayesD sub-models of Wellmann and Bennewitz  differ iF is described in detail in [A full description of BayesD can be found in . Only esetail in . Conditiis large . This prFor the joint posterior distribution and the Markov chain, which was generated by Gibbs sampling, see . BayesD pLD for analysis of the simulated data. For We chose For inference of association, we used the posterior probability of the window association (WPPA) criterion proposed by Fernando and Garrick  and Fernmentclass2pt{minimnto Eqs.  if estimmentclass2pt{minimnto Eqs.  is then For each window, the ratio Expectations rding to , this coA causal gene is mapped if at least one window within a region of 1 cM surrounding the gene shows a WPPA above the threshold. For each simulated trait, power to map a causal gene was calculated by dividing the number of mapped causative genes by the number of simulated causative genes that showed an effect greater than expected under the assumption that the genetic variance is distributed equally across the genome. Hence, very small causative genes were not counted. This guarantees that the upper bound of the power is 1, as it should be. From the definition of DGAT1 gene has a major effect in this population and dominance is important [The models were also applied to a Fleckvieh dairy cattle dataset, which is described in detail by Ertl et al. . In briemportant . Therefomportant . Paramet effects .Results of the power evaluations from the simulated datasets are in Table Power increased with SNP density. For example, for BayesC, a WPPA of 0.95 and a window size of 0.5, L-power was equal to 0.35, 0.39, 0.47, and 0.52 for SNP densities of 0.5k, 1k, 2k, and 7k, respectively. The same pattern was observed for BayesD.Power also increased as window size increased. For example, L-power was equal to 0.42, 0.47, and 0.52 for window sizes of 0.25, 0.5 and 1 cM respectively . This pattern held true for all genetic configurations and for both methods.Application of BayesD improved the power compared to BayesC for almost all genetic configurations. For example, for a WPPA of 0.95 and a window size of 1 cM, L-power of BayesC was equal to 0.35, 0.44, 0.52, and 0.55 and that of BayesD was equal to 0.41, 0.5, 0.53, and 0.57 for SNP densities of 0.5k, 1k, 2k and 7k, respectively. In general, it appeared that the superiority of BayesD over BayesC declined as SNP density increased. For a 7k SNP density, and a window size of 0.25, BayesC resulted in slightly greater power than BayesD.Results of the evaluation of mapping precision are in Table DGAT1 is located and a clear signal on chromosome 10, although this was below the threshold levels used in this study. No other WPPA was above the threshold levels used in this study, which indicates that either no other genes with a larger effect are segregating in this population, or the sample size of the data set is too small, or both.Plots of WPPA along the chromosomes are in Fig. Closer inspection of the WPPA plots revealed some differences between the two methods. BayesD produced several extra signals, although far below the threshold levels used in this study. Examples are on chromosomes 6, 11, and 21. In addition, the average WPPA across the genome was slightly higher for BayesD than for BayesC. In Fig. Multi-marker Bayesian methods for association analyses were compared using simulated and real data. The simulation protocol regarding genetic architecture followed our current understanding of quantitative traits with regard to number of segregating causal mutations and their additive and dominance effects. In a recent study , we condOnly one chromosome was simulated because the MCMC-based analyses were computationally demanding and replicated simulations were performed. It is possible that the power that would result from the simulation of multiple chromosomes would be somewhat reduced, but this would not alter the general findings of our study. However, the results obtained by using real data revealed that it is possible to also apply these methods in the case of genomes that consist of numerous chromosomes, and for which 630k SNPs are available. Due to the stochastic nature of the effects during the simulation of the traits, the dominance variance calculated as the proportion of the phenotypic variance ranged from 0.01 to 0.29, with a median of 0.08. These values are consistent with those reported by Bolormaa et al. , i.e. prThe results showed that method BayesD increased power to map QTL compared to BayesC in almost all analyses because it uses dominance variance as an additional source of genetic variance. This increased power can also be deduced from the results of the analyses of the real dairy cow dataset Fig. , where BFigure Since dominance is an interaction effect of the two alleles at a locus, their effects are captured in the association analysis by matched haplotype pairs, i.e. diplotypes. Diplotypes show a faster breakup around a focal point in the genome compared to haplotypes. Hence, BayesD was expected to improve the mapping precision as well, but the observed improvement was only small and was more pronounced for smaller window sizes.For a high SNP density and a small window size, BayesC outperformed BayesD with regard to power. This intuitively unexpected result can be explained by the fact that, in BayesC one effect is estimated per SNP, whereas in BayesD two effects are estimated per SNP. Thus, with BayesD, the effect of a causative mutation may be spread over more very closely-linked SNPs than for BayesC, and some SNPs may even be outside the window, if the window size is small.For BayesC, only the additive genetic variance and the residual variance need to be known, which can usually be estimated from the data with high precision. In BayesD, dominance variance and inbreeding depression also need to be known. With the use of genomic data it might be possible for most traits in most populations to estimate them precisely, at least for the dominance variance , 13. Comthe data  but the the data , or by uthe data , in whicOur simulation study was not designed to determine whether the WPPA controls the proportion of false positives at the desired level. This hampered the comparison of WPPA between BayesC and BayesD in a formal way. Instead, we searched for elevated WPPA (at the lowest threshold level of 0.85 and even lower) in chromosomal regions of about 10 cM that had no simulated causal mutation. In very exceptional cases, an elevated WPPA was observed in these regions without any differences between BayesC and BayesD. Hence, it appears that WPPA controls the proportion of false positives in the simulation study at a low level for both methods. This might be due to the small number of degrees of freedom that was used for the Instead of drawing inferences from SNPs in windows, the posterior probability of the effect of a specific SNP being drawn from the distribution with the larger variance could have been used for inference purposes. However, in the study of Sahana et al. , this reA sliding-window-based approach was used by moving the window boundaries one SNP forward along the chromosome. This resulted in as many windows as SNPs included in the analysis, and also in the same number of WPPA, which are highly correlated for consecutive windows. Alternatively, the chromosome could have been divided into non-overlapping windows. This would reduce the number of windows but introduces the problem of arbitrarily setting the window boundaries. It is possible that such boundaries will break a chromosomal region that harbours a causative mutation into two or more distinct windows, which would reduce the power to map the mutation. The choice of windows deserves additional investigations that take the LD structure along the genome into account . AnotherInferences were drawn by using the WPPA criterion and using estimates of genomic variance within windows. If inference on the importance of dominance is of interest, the same criterion can be used by using estimates of dominance variance within windows. A straightforward strategy would be to map causative genes using estimates of within-window genomic variance, as done in this study, and then test the importance of dominance by using the within-window estimate of dominance variance.Given that the scaling argument of  also holThe application of BayesD for GWAS on simulated quantitative traits with realistic dominance effects resulted in increased power compared to BayesC. The increase in power was between −2 and 8% for causative genes that explain more than 2.5% of the genetic variance. This trend in increased power was also observed in the results from the real data analyses. In addition, by examining the within-window estimates of genomic dominance variance, BayesD allows for inference about the magnitude of dominance effects at significant associations, which remains hidden in BayesC analyses. Mapping precision was, however, not substantially improved by BayesD. If the aim is to map mutations with medium and small effects, large datasets that include several thousands of individuals are needed.


Genomic regions of autozygosity (ROA) arise when an individual is homozygous for haplotypes inherited identical-by-descent from ancestors shared by both parents. Over the past decade, they have gained importance for understanding evolutionary history and the genetic basis of complex diseases and traits. However, methods to infer ROA in dense genotype data have not evolved in step with advances in genome technology that now enable us to rapidly create large high-resolution genotype datasets, limiting our ability to investigate their constituent ROA patterns.We report a weighted likelihood approach for inferring ROA in dense genotype data that accounts for autocorrelation among genotyped positions and the possibilities of unobserved mutation and recombination events, and variability in the confidence of individual genotype calls in whole genome sequence (WGS) data.Forward-time genetic simulations under two demographic scenarios that reflect situations where inbreeding and its effect on fitness are of interest suggest this approach is better powered than existing state-of-the-art methods to infer ROA at marker densities consistent with WGS and popular microarray genotyping platforms used in human and non-human studies. Moreover, we present evidence that suggests this approach is able to distinguish ROA arising via consanguinity from ROA arising via endogamy. Using subsets of The 1000 Genomes Project Phase 3 data we show that, relative to WGS, intermediate and long ROA are captured robustly with popular microarray platforms, while detection of short ROA is more variable and improves with marker density. Worldwide ROA patterns inferred from WGS data are found to accord well with those previously reported on the basis of microarray genotype data. Finally, we highlight the potential of this approach to detect genomic regions enriched for autozygosity signals in one group relative to another based upon comparisons of per-individual autozygosity likelihoods instead of inferred ROA frequencies.This weighted likelihood ROA inference approach can assist population- and disease-geneticists working with a wide variety of data types and species to explore ROA patterns and to identify genomic regions with differential ROA signals among groups, thereby advancing our understanding of evolutionary history and the role of recessive variation in phenotypic variation and disease.The online version of this article (doi:10.1186/s12864-017-4312-3) contains supplementary material, which is available to authorized users. Genomic regions of autozygosity (ROA) reflect homozygosity for haplotypes inherited identical-by-descent (IBD) from an ancestor shared by both maternal and paternal lines. Common ROA are a source of genetic variation among individuals that can provide invaluable insight into how population history, such as bottlenecks and isolation, and “sociogenetic” factors, such as frequency of consanguineous marriage, influence genomic variation patterns. Population-genetic studies in worldwide human populations over the past decade have found ROA ranging in size from tens of kb to multiple Mb to be ubiquitous and frequent even in ostensibly outbred populations –28 and tIn contemporary human populations, increased risks for both monogenic –84 and cPLINK . An intuitive explanation for this correction is that when a number of SNPs are highly correlated they provide redundant information. By weighting the log-likelihood for SNP k as a function of its correlation with all other SNPs within window w it contributes only the unique autozygosity information it possesses to wLOD.Here, we adapt the approach of Chen et al.  to incork by the probability of no recombination events having occurred within the genomic interval bounded by SNP k − 1 and SNP k in the last M generations, calculated based upon their genetic map position g (in Morgans) as previously described ). Each simulated dataset consisted of a single 250 Mb chromosome upon which ~750,000 polymorphic single-nucleotide variants (SNVs) segregate, consistent with the SNV density and length of chromosome 1 in The 1000 Genomes Project Phase 3 WGS data.To evaluate the sensitivity and specificity of the escribed  except t29 years ). ScenarwLOD estimator considering windows of between 50 and 500 SNPs (in 10 SNP increments), and a proportion of overlapping autozygous windows used to construct ROA of between 0 and 50% (in 1% increments). We then calculated three measures of how well inferred ROA agreed with true ROA reported by the simulation program. First, we calculated the power of the wLOD method to detect true ROA, defined here as the total length of true ROA that is overlapped by inferred ROA divided by the total length of true ROA. Second, we calculated its false positive rate as the total length of inferred ROA that does not overlap with true ROA divided by the total length of inferred ROA. Finally, for all true ROA detected with the wLOD method, we calculated the ratio of inferred ROA length and true ROA length for all ROA. Here, ratios greater than one indicates a tendency to overcall ROA by falsely including non-autozygous regions near the boundaries of true ROA, while ratios below one indicate a tendency to instead undercall an ROA by falsely excluding true autozygous regions near the boundaries of true ROA  = 3.85) with a window size of 50 SNPs―and therefore delineated by a few erroneous autozygous windows that progressively fail to meet the required threshold during ROA calling as the window overlap fraction increases. Once window size reaches ~90 SNPs, the wLOD estimator is able to distinguish autozygosity from homozygosity-by-chance with great precision. Conversely, numbers of false negative ROA calls increase as a function of window size and overlap fraction  and OmniExpress-24  BeadChips and Affymetrix’s Genome-Wide Human SNP 6.0 Microarray . In addition, we included subsets with SNV densities consistent with the genotyping platforms used by ROA studies in cattle and dogs: Illumina’s Bovine HD  and Canine HD  BeadChips. ROA inference accuracy was evaluated exactly as described above for the WGS datasets at the optimal window size and overlap fraction determined separately for each SNV density and demographic scenario . However, false discovery rates do increase dramatically with decreasing SNV density, particularly for smaller ROA . Fitting these averages against the natural logarithm of average SNV density D across all 50 replicates of their respective SNV subset, this suggests that as a rule of thumb future studies apply the wLOD method at a window size equal to 16.400 × loge(D) + 218.020 and an overlap fraction equal to 0.0736 × loge(D) + 0.8063. Based upon these equations, and calculating SNV density as the number of autosomal SNPs on the microarray divided by the total length of the target species’ autosomal genome, guideline settings for window size and overlap fraction with the commonly used human and non-human genotyping microarrays are: 111 SNPs (33%), 103 SNPs (29%), 85 SNP (21%), 81 SNPs (19%), and 59 SNP (9%) for Illumina’s HumanOmni5, HumanOmni2.5, Bovine HD, OmniExpress, and Canine HD BeadChips, respectively, and 85 SNPs (21%) for the Affymetrix Genome-Wide Human SNP 6.0 Microarray. Considering the range of autosomal SNVs observed in the WGS data available for the 26 populations in Phase 3 of The 1000 Genomes Project  a windowLOD method to be well powered to detect ROA in genetic datasets consistent with WGS and microarray-based genotyping. We next evaluated how the power and false discovery rate of the wLOD method compared with those of three current methods designed specifically to detect ROA in dense genotype data using the datasets simulated above: the original LOD method, the naïve genotype counting method implemented in PLINK  and all values of p lie within the interval . To begin, we created a backbone of genetic and physical map positions onto which we will place all other positions, randomly drawing (gmax/θ) + 1 values of g and assigning them in increasing order to p in the range [1. . (gmax/θ)] (i.e. every Mb). Next, we randomly chose N values of p to be predetermined polymorphic SNVs, and then randomly assigned each a value of g based upon the backbone interval in which it was located, again ensuring that values of g always increase as a function of p. Finally, all values of p that were not among the set of predetermined SNVs were assigned a value of g through interpolation onto the construct created by the values of p and g assigned to the predetermined SNVs. This approach created a non-uniform relationship between physical and genetic map distance along the simulated chromosome that is similar to that observed on real human chromosomes (not shown).If we let μ × , where μ is mutation rate. The base pairs to be mutated were then chosen at random from all (gmax/θ) × 1, 000, 000 possible positions without replacement. Mutations were tracked and then incorporated into the genotypes of individuals in the analyzed dataset; all monomorphic positions were removed during dataset construction.To extend the method of Kardos et al. to enable any base pair on the simulated chromosome to mutate, for each individual in each generation, the number of mutations that occur during each meiosis was drawn from a Poisson distribution with mean gmax to 325 cM, θ to 1.3 cM/Mb [μ to 1.18 × 10−8 [θ and μ by a factor of 10 to increase genetic diversity in the final generation [N was chosen separately for each simulated scenario such that the final number of polymorphic SNVs in the dataset (both predetermined and de novo) was ~750,000; N = 725,000 for scenario 1 and N = 650,000 for scenario 2. Because predetermined polymorphic SNVs can become fixed over the course of the simulation, their numbers in the analyzed datasets lay between 679,256 and 717,855  for scenario 1 and between 633,582 and 638,675  for scenario 2. The simulated WGS datasets used in the analyses contained 50 individuals randomly chosen from among the 75 present in the final generation with genotypes for 709,862–746,963 polymorphic SNVs in scenario 1 and 737,957–748,572 polymorphic SNVs in scenario 2. The 125K, 80K, 50K, and 18K subsets of the WGS datasets contained between 117,113–123,766, 74,953–79,211, 46,846–49,507, and 16,865–17,823 polymorphic SNVs, respectively, for scenario 1, and between 121,833–122,815, 77,973–78,602, 48,733–49,126, and 17,544–17,686 polymorphic SNVs for scenario 2.In all simulations, we set .3 cM/Mb , and μ t8 × 10−8 , and scaneration . N was cM was set to these average values when analyzing their respective datasets.To better mimic real genetic datasets, we randomly introduced genotyping errors separately into each simulated dataset at a rate of 0.001, a conservative value that is similar to but slightly higher than the average rate of genotype discordance across 1693 individuals between genotypes in their WGS data and those obtained at the exact same SNVs with the Illumina HumanOmni2.5 BeadChip , and we PLINK, we allowed at most 2% of SNPs to have heterozygous genotypes and 5% of SNPs to have missing genotypes for a window to be inferred to be autozygous [LOD method and BCFtools were applied using the same allele frequency estimates and error rate ε as the wLOD method, while BCFtools additionally incorporated genetic map positions and performed Viterbi training with initial transition probabilities between autozygous and non-autozygous states and vice versa of 6.6 × 10−8 and 5.0 × 10−9, respectively, to optimize its underlying model prior to ROA inference [For tozygous . The LODnference .wLOD scores at all window sizes considered. To account for sample-size differences among populations, we used a resampling procedure to estimate the allele frequencies, sampling 100 non-missing alleles with replacement and calculating allele frequencies from these 100 alleles. As a consequence of the resampling procedure, it was possible for an individual to possess an allelic type whose frequency was estimated to be 0 in the sample of 100 alleles. SNV positions at which this scenario was encountered were treated as missing when calculating wLOD scores for all windows containing the positions in individuals that had the allelic type of frequency 0.To minimize the number of variables that varied in within-dataset comparisons, we used a single set of allele frequencies when calculating wLOD estimator . The genetic map position of each marker in the WES and WGS datasets was determined by interpolation onto the Rutgers linkage-physical map [In the recombination rate correction applied in the ator Eq. , the genical map  based onwLOD score distributions used to determine the autozygosity score thresholds in the WGS dataset considered only twenty individuals chosen at random. Based on our investigation into the effect of sample size on score threshold  [R statistical software (v.3.3.3) [G) were calculated using the function mclustBIC, while final classification under the five component model was performed using the function Mclust. Violin plots [We ran unsupervised Gaussian fitting of the ROA length distribution using the  (v.5.2)  in the Rv.3.3.3) , allowinin plots  of totalr) of their mean ROA frequencies across windows. We then applied MDS to this matrix using cmdscale in R.The frequency at which each SNV was present in ROA in each population was calculated as described in Pemberton et al. . To compFST among populations calculated with our WGS dataset and the method of Hudson et al. [FST was evaluated with the Procrustes method [We compared population patterns in the MDS based on ROA frequencies to an MDS based on a matrix of pairwise n et al.  accordinn et al. . The sims method .nSL selection scores [th, 2014), and nSL values for each of the 26 populations were calculated in the WGS dataset considering only SNVs with MAF > 0.05 and normalization of unstandardized scores in 100 genome-wide frequency bins with selscan [nSL were performed as described in Pemberton et al. [For each ROA length class, we investigated recombination rate and haplotype-based n scores  for corrn scores  Additional file 2: Tables S1-S9.Supplementary tables and their footnotes. (PDF 867 kb)