Hoxa1 coding region with its paralog Hoxb1 in mice (Mus musculus) residing in semi-natural enclosures. Previously, this Hoxa1B1 swap was reported as resulting in no discernible embryonic or physiological phenotype , despite the 51% amino acid sequence differences between these two Hox proteins. Within heterozygous breeding cages no differences in litter size nor deviations from Mendelian genotypic expectations were observed in the outbred progeny; however, within semi-natural population enclosures mice homozygous for the Hoxa1B1 swap were out-reproduced by controls resulting in the mutant allele being only 87.5% as frequent as the control in offspring born within enclosures. Specifically, Hoxa1B1 founders produced only 77.9% as many offspring relative to controls, as measured by homozygous pups, and a 22.1% deficiency of heterozygous offspring was also observed. These data suggest that Hoxa1 and Hoxb1 have diverged in function through either sub- or neo-functionalization and that the HoxA1 and HoxB1 proteins are not mutually interchangeable when expressed from the Hoxa1 locus. The fitness assays conducted under naturalistic conditions in this study have provided an ultimate-level assessment of the postulated equivalence of competing alleles. Characterization of these differences has provided greater understanding of the forces shaping the maintenance and diversifications of Hox genes as well as other paralogous genes. This fitness assay approach can be applied to any genetic manipulation and often provides the most sensitive way to detect functional differences.Here we assess the fitness consequences of the replacement of the  Mus musculus) [Approximately 10% of genes show minimal-to-no phenotypic consequences when disrupted in mice (usculus) ,3. OftenMuch empirical and theoretical effort has been applied to understanding how duplicated genes can be maintained through evolutionary time. When initially duplicated, one copy is likely to accumulate degenerative mutations (in either protein coding or regulatory sequences), which are invisible to selection, leading to non-functionalization . DespiteDrosophila, Hox genes encode developmentally important transcription factors that provide insightful clues to mechanisms of gene and genome duplications during the evolution of metazoans. In mice and humans, there are 39 Hox genes, arranged in four tightly linked clusters  on four different chromosomes, each harboring 9–11 genes belonging to 13 different paralogous groups (Hox1-Hox13). The classic view is that these four Hox clusters have derived from a single early chordate cluster in two rounds of whole genome doubling [Originally discovered in doubling , althougdoubling .Hoxa1 and Hoxb1, both of which are involved in the patterning of the brainstem, are functionally interchangeable at the protein level (via proximate assessments).Molecular properties of Hox genes from different paralogous groups have diverged significantly. In addition to displaying differential temporal and anterior-posterior expression patterns, different Hox paralogs recruit distinct DNA binding co-factors. Moreover, their DNA binding domains, the homeoboxes, are not functionally interchangeable in the development of most tissues, as demonstrated in elegant homeobox-swapping experiments by Zhao and Potter ,10. ThesHoxa1 knockout mice, expression of Hoxb1 and other downstream genes is altered, the brainstem respiratory circuits are malformed, and Hoxa1 neonatal knockouts die [Hoxb1 knockouts are viable, but display facial paralysis [Hoxa1B1 swapped mice, mutants expressing HoxB1 protein from both Hoxa1 alleles, show no changes under laboratory conditions; this is despite a 15% amino acid sequence divergence at the homeodomains and merely 49% total identity [Xenopus, in which functional redundancy across Hox paralogous group 1 was demonstrated in a variety of proximate measures [In outs die ,15. Convaralysis . Intriguidentity ,17. Thusmeasures .Hoxb1A1 swap compared to controls using our organismal performance assay (OPA) model system [Hoxb1A1 swap, we observed that males homozygous for the swap acquired fewer territories, a key fitness component, and that a deficiency of both Hoxb1A1 homozygous and heterozygous offspring was present in the generation of offspring born within OPA enclosures, despite detailed molecular studies indicating functional interchangeability. These findings suggest that Hoxa1 and Hoxb1 are phenotypically divergent, and consequently, have incomplete redundancy at the organismal level.In a previous experiment, we assessed the fitness consequences of mice being homozygous for a l system . OPAs arl system –26. SpecHoxa1 locus (Hoxa1B1)—relative to control mice bearing an appropriate genetic control. During these 25-week OPA trials we take measures of male competitive ability of founding individuals and assess allelic frequencies and Hoxa1 genotypes of offspring born within enclosures for numerical deficiencies or excesses. Additionally, breeding cage measurements of litter size and genotypic frequencies of offspring from heterozygous mates are taken, allowing us to evaluate the role of naturalistic environments in revealing fitness differentials. Such assessments of reciprocal swaps are common in developmental literature , ,27, Hoxae /B1(g)–possessing 129x C57BL/6 hybrids, generated by homologous recombination  were crossed (n = 58) to establish the F2 generation (Hoxa1B1(g)/B1(g) homozygotes, here on referred to as Hoxa1B1 founders, were selected for OPA assessment. Likewise, a control lineage of mice was bred by crossing 17 Hoxa1+(g)/+(g) 129 x C57BL/6 hybrid mice with the same wild-derived stock. The resulting F1Hoxa1+(g)/+ generation (n = 85) were then crossed to produce the F2 generation (Hoxa1+(g)/+(g) homozygotes, here on referred to as control founders, were selected as OPA founders. Prior to OPA release, all animals were housed according to standard protocols under a 12:12 h light:dark cycle with food and water available ad libitum. All protocols were approved by the animal care guidelines of the IACUC at the University of Utah .Strains of inbred laboratory mice do not possess the natural behaviors required for OPA assessment ,29; therere bred . A Hoxa1eference ), with gr et al. . The resneration . Only coneration . Only coHoxa1 genotype was determined using a three primer PCR amplification system where a 3' common primer (5'- TCA CCA TCA CCA CCA TCA C) anneals between exons 1 and 2 within the bridging intron and specific 5' primers, which anneal within exon 1—for Hoxa1+/+ (5'-ACT CCT TAT CCC CTC TCC AC) and for Hoxa1B1(g)/B1(g)(5'-CAA GAG AAA CCC ACC TAA GAC)—yield a 381 bp and 284 bp fragment respectively (5'-AGA TGG GAC GAG AAA GGA AG) and a 5' specific primer for Hoxa1+(g)/+(g) (5'-ACA ACC ACT ACC TGA GCA A) located within the tauGFP site and for Hoxa1+/+ (5'- TGG CAG CGA TGA GAA AAC), located 5' of where the tauGFP insertion within animals possessing it, yield a 298 bp and 225 bp fragment respectively, which were visualized on 5% polyacrylamide gels  or two “suboptimal” territories (with nest boxes exposed to the light). Descriptions of enclosure, including photographs and associated methods, have been provided elsewhere in more detail [OPA enclosures are 30 me detail ,23–25.2 individuals, 10 males and 20 females, with equal numbers of Hoxa1B1 and control founders within each population. Founders were 38.4 ± 0.9 (mean ± SD) weeks of age for females and 37.8 ± 0.3 weeks for males. Relatedness was avoided within populations and no individuals were related at or above the sibling level. To prevent incidental breeding before the establishment of social dominance networks by males, untreated females from our stock wild-derived colony were initially released with male founders allowing territorial formation prior to release of female founders. At the start of the 25-week OPA trial untreated females were removed and female founders released.Three independent OPA enclosures were founded by 30 FPopulation-level reproductive success was determined for founders of each treatment by harvesting tissue samples gathered during “pup sweeps”, in which pups born during the previous cycle were removed from the population and euthanized. Sweeps occurred every five weeks to prevent offspring born in enclosures from becoming breeders.B1 and control males were gathered for each population throughout the study.Prior to release into enclosures, founders of both sexes were implanted with unique passive integrated transponder tags . Location data are gathered via a set of antennae and readers  placed at each of the feeders and data are recorded with data-logging software . Dominance was assigned when a male had more than 80% of all male readings at a single feeder over the course of a multi-day reader session. Paired measures of the number of territories controlled by Hoxa12 offspring were assessed in Hoxa1A1 treatment and control lineage heterozygote breeding cages. Each homozygote genotype was directly compared to the other and heterozygote counts were compared to the summation of both homozygote counts. A generalized linear mixed model (GLMM) with a Poisson distribution and a logarithmic link was used, in which genotype was modeled as a fixed effect and individual breeding cage was modeled as a random effect. Hoxa1B1 treatment lineage models were based on 116 observations from 58 breeding cages, while both models for the control lineage were based on 170 observations from 85 cages. Litter sizes between the lineages were compared with a Mann-Whitney U test.Deviations from expected genotypic frequencies of FHoxa1B1(g) and control Hoxa1+(g) alleles of offspring born within OPAs a GLMM assuming a Poisson distributions and using a logarithmic link was employed. We predicted population-level allelic counts by modeling the fixed effects of allele, time, and their interaction, while population was modeled as a random effect with a generated random intercept and slope. Allelic counts were measured five times, at five-week intervals, for a total of 30 observations across the three populations and the intercept was set at the grand mean (week 15).To examine the counts of the mutant Hoxa1B1(g)/B1(g)vs. Hoxa1+(g)/+(g)), time, and their interaction, while population was modeled as a random effect with a generated random intercept. Offspring genotypes were measured five times, at five-week intervals, for a total of 30 observations across the three populations and the intercept was set at the grand mean (week 15). In the second model, four genotype groups  count of heterozygotes based upon each of the homozygote counts) were assessed with 15 observations available for each. Time, genotype, and their interaction were modeled as fixed effects and population was modeled as a random effect with a random intercept and slope.Similar to the analysis of genotypes from breeding cages, offspring counts from OPAs were modeled over time using two GLMMs with Poisson distributions and logarithmic links. In the first model, we predicted population-level fitness by modeling the fixed effects of genotype , with population modeled as a random effect. Territorial occupation was assessed across the study for a total of 70 observations. The intercept of the model was set at the grand mean (week 12.8).glmer function of the ‘lme4’ library [All GLMMs were fit in R using the  library ,31. For 2 offspring produced within both Hoxa1B1 and control lineage heterozygous breeding cages conformed to Mendelian expectations and litters from both lineages were of similar size (B1 lineage heterozygous breeding cages (n = 58), no difference was observed in the count of homozygous offspring possessing the two genotypes . Similarly, in control lineage heterozygous breeding cages (n = 85) no differences were observed between the two homozygote counts , nor did the count of heterozygotes differ from that of summed homozygotes . Finally, F2 litters did not differ in size between Hoxa1B1 and control lineages .Genotypic frequencies of Flar size . In HoxaHoxa1B1(g) allele was only 87.5% as common as the control allele (Hoxa1B1(g) alleles per population per sampling, while for the control Hoxa1+(g) allele there were 56.3 ; this difference was statistically significant , but this increase did not differ between the two alleles . SEs are asymmetrical, as they are back transformed from logarithmic data.Within offspring born in OPA enclosures the mutant l allele . SpecifiB1 founders produced only 77.9% as many pups as controls over the course of the study within OPAs (Hoxa1B1(g)/B1(g) offspring per sampling per population, while there were 16.0  Hoxa1+(g)/+(g) offspring; this difference was statistically significant  nor a time-by-genotype interaction  influenced offspring counts, suggesting a consistent rate of reproduction across the study.As measured by homozygous offspring, Hoxa1hin OPAs . SpecifiHoxa1B1(g)/+(g) heterozygotes per sampling per population, while there were 28.3  homozygotes; this difference was statistically significant  nor time-by-genotype  were detected on genotypic counts. Heterozygote levels were below those predicted based on the count of Hoxa1+(g)/+(g) pups , but did not differ from predictions based on Hoxa1B1(g)/B1(g) offspring .Relative to summed counts of homozygotes, a 22.1% deficiency of heterozygous offspring was detected over the course of the study within OPAs . SpecifiB1 and control founders ; however, the probability that a Hoxa1B1 male controlled a territory increased over time relative to controls  leading to a situation in which the pattern observed initially was reversed by the study’s conclusion. Finally, there was no differential longevity between Hoxa1B1 and control founders, as all founders (n = 90) survived until the end of the 25-week study.Within OPAs, no uniform difference in territorial ownership across the study was observed between male Hoxa1founders . InitialB1 founders were outcompeted by controls within OPA enclosures as they produced only 77.9% as many offspring relative to controls as measured by homozygous pups; furthermore, a 22.1% deficiency of heterozygous offspring was observed in enclosures. Combined, the homozygote and heterozygote deficiencies resulted in the mutant Hoxa1B1(g) being only 87.5% as frequent as the control allele in offspring born within OPAs. These OPA observations are in contrast to measures in standard laboratory breeding cages where neither a difference in litter size nor genotypic frequencies were observed between heterozygous pairs in the Hoxa1B1 and control lineage. Typically within OPAs differential reproductive output between experimental groups is driven by either differential longevity or male competitive ability; however, neither of these fitness components differed between Hoxa1B1 and control founders. Though an overall trend emerged that male control mice were more likely to dominate a territory than Hoxa1B1 males, the instability of the pattern over time makes it difficult to link competitive ability to the observed reproductive deficiency. Furthermore, as all founders survived until the termination of the study, differential reproduction cannot be explained by mortality.Hoxa1B1 and control founders, in the broadest sense, could be due to either litters containing fewer pups or decreased frequency of litter production. As Hox genes have key roles in development it is possible that embryonic lethality could be reducing the size of litters born to Hoxa1B1 founders, though this is not supported by cage measures of genotypic frequency. Hoxa1B1 founders could be having fewer litters throughout the study due to a variety of factors such as decreased resource acquisition, or discrimination during mate choice; however, no evidence is available to specifically support that there are fewer litters produced. Thus, the proximate underpinnings of the fitness differential identified here require further investigation.The reproductive differential between Hoxa1Hoxb1A1 swap [The results of this study are consistent with our previous investigation using OPAs to assess the fitness consequences of the reciprocal 1A1 swap . In thatHoxa1B1(g)/B1(g) genotype in the mixed inbred C57BL/6 x 129 background kept in laboratory conditions. The distortion of Hoxa1B1(g)/B1(g) segregation was noticeable, although it did not reach statistical significance. We argue that this discrepancy is due to the pivotal role of Hoxa1 in the hindbrain development, being positioned in the center of a complex regulatory network of upstream and downstream factors that can modify the severity of the mutant or hypomorphic phenotype [In regards to genotypic frequencies observed in heterozygous breeding cages, neither study found deviations from Mendelian expectations for either the experimental or control lineages generated in this research. In the original report, Tvrdik and Capecchi  observedhenotype –35.Hoxa1 function is corroborated by the heterogeneity of human syndromes involving HOXA1 mutations. Homozygous HOXA1 loss of function was found in consanguineous families from three ethnically unrelated populations of Saudi Arabian, Turkish, and Native American descent. These HOXA1 mutations result in two overlapping, but distinct syndromes which have been described as the Bosley-Salih-Alorainy syndrome and the Athabaskan brainstem dysgenesis syndrome. The differences in manifestation of the two syndromes are most likely attributable to ethnic-specific genetic modifiers present in these human populations [The strong influence of genetic background on ulations –39.Two previous studies supporting functional redundancy of Hox paralogous group 1 proteins have been conducted which carefully assessed multiple proximate endpoints including expression levels and histological confirmation of normal tissue throughout development ,18. The Hox genes have been studied intensely to further our understanding of how duplicated genes are maintained across evolutionary time, with the leading explanation for the case of Hox paralogs being through the process of sub-functionalization [lization . ImportaBeyond inquiries concerning the maintenance of duplicated genes, many questions in both genetics and evolutionary biology require experimentally derived fitness measures. Specifically, within areas of research including facultative sex ratio biasing, Hamilton-Zuk sexual selection, and the benefits of genome-wide heterozygosity, the need for experimentally derived fitness measures has already been acknowledged –42. ThouHoxa1B1 swap relative to controls, adversity that was not observed previously by studies focusing solely on proximate endpoints. With OPAs, we and others have been able to detect adversity to numerous exposures  and genetic manipulations  that were missed by other, often molecular, assays [Using the OPA model system we are able to quantify negative fitness consequences in mice homozygous for a , assays –26. Succ, assays . The illS1 Table(PDF)Click here for additional data file.S2 Table(PDF)Click here for additional data file.S3 Table(PDF)Click here for additional data file.


To determine whether more years spent in education is a causal risk factor for myopia, or whether myopia is a causal risk factor for more years in education.Bidirectional, two sample mendelian randomisation study.Publically available genetic data from two consortiums applied to a large, independent population cohort. Genetic variants used as proxies for myopia and years of education were derived from two large genome wide association studies: 23andMe and Social Science Genetic Association Consortium (SSGAC), respectively.67 798 men and women from England, Scotland, and Wales in the UK Biobank cohort with available information for years of completed education and refractive error.Mendelian randomisation analyses were performed in two directions: the first exposure was the genetic predisposition to myopia, measured with 44 genetic variants strongly associated with myopia in 23andMe, and the outcome was years in education; and the second exposure was the genetic predisposition to higher levels of education, measured with 69 genetic variants from SSGAC, and the outcome was refractive error.Conventional regression analyses of the observational data suggested that every additional year of education was associated with a more myopic refractive error of −0.18 dioptres/y . Mendelian randomisation analyses suggested the true causal effect was even stronger: −0.27 dioptres/y . By contrast, there was little evidence to suggest myopia affected education . Thus, the cumulative effect of more years in education on refractive error means that a university graduate from the United Kingdom with 17 years of education would, on average, be at least −1 dioptre more myopic than someone who left school at age 16 (with 12 years of education). Myopia of this magnitude would be sufficient to necessitate the use of glasses for driving. Sensitivity analyses showed minimal evidence for genetic confounding that could have biased the causal effect estimates.This study shows that exposure to more years in education contributes to the rising prevalence of myopia. Increasing the length of time spent in education may inadvertently increase the prevalence of myopia and potential future visual disability. Myopia, or short-sightedness, is one of the leading causes of visual disability worldwide, and its prevalence is increasing rapidly.For more than a century, myopia has been associated with higher levels of educational attainment,Mendelian randomisation is a type of instrumental variable analysis23andMe—Pickrell et alSocial Science Genetic Association Consortium (SSGAC)—Okbay et alUK Biobank—Cross sectional data from the baseline assessment of the UK Biobank project was collected between 2006 and 2010.Education—We determined the time spent in education by questionnaire as defined by the question for age of completed full time education in UK Biobank (n=336 826 participants completed the questionnaire at the baseline visit). The question was ascertained only for participants who did not have a college or university degree. To harmonise the educational outcome measure in UK Biobank (time spent in education) with the number of years spent in schooling (EduYears) variable in the SSGAC study,Refractive error—Measures of visual function were not performed from the start of recruitment for UK Biobank. Consequently, only a subset of participants underwent measurements of refractive error (n=127 412). This was measured by non-cycloplegic autorefraction  after removal of spectacles or contact lenses. Although cycloplegic eye drops were not used , only adults in whom the effects of accommodation would be minimal were recruited to UK Biobank.In total, 69 798 participants had valid education, refractive error, and genetic data available .The genetic data in UK Biobank underwent rigorous quality control procedures and was phased and imputed against a reference panel of Haplotype Reference Consortium (HRC), UK10K, and 1000 Genomes Phase 3 haplotypes.Using linear regression adjusted for sex and age in UK Biobank, we assessed observational associations between refractive error and years spent in education. We then repeated the regression with adjustment for additional potentially confounding variables . The authors identified 74 variants associated with educational attainment in SSGAC. Five variants  were not in the HRC panel, leaving 69 variants for use as instrumental variables (see supplementary data table).Okbay et ala) and non-effect allele (A) dosages. Allele scores were calculated by summing the product of the weights and dosages across all n variants (see equations).For each trait we combined multiple genetic variants into a single weighted allele score. Compared with individual variants, this score has been shown to improve the coverage properties and reduce the bias of instrumental variable estimates.We calculated the proportion of variance in the phenotype variable explained by the allele score instrumental variable, by regressing the phenotype on its respective allele score.ivpack.http://cnsgenomics.com/shiny/mRnd/).Mendelian randomisation was implemented using the two stage least squares method in the R package We used confounding bias plotsgithub.com/MRCIEU/TwoSampleMR).To investigate the degree of bias in the initial causal estimates due to pleiotropic effects, we used two sensitivity analyses (mendelian randomisation-Egger and weighted median mendelian randomisation). Mendelian randomisation-Egger is not valid for studies in which the instrumental variable-exposure and instrumental variable-outcome associations are calculated in the same sample . Therefore, we ran the mendelian randomisation-Egger as a split sample analysis, by randomly splitting the sample in half (groups A and B). The supplementary data table shows the associations of the variants and time spent in education and refractive error for each group. Mendelian randomisation-Egger and weighted median methods were implemented using the R package TwoSampleMR  of the variance in average mean spherical equivalent refractive error of participants in UK Biobank and the education allele score explained 0.71% (F=464) of the variance in time spent in education. We selected these genetic variants to use as instrumental variables because of their robust association with time spent in education and myopia, allowing us to construct strong aggregate instrumental variables for making mendelian randomisation inferences. The large F statistics suggested that these analyses would not be affected by weak instrument bias.The myopia allele score explained 4.32% (v −0.18 dioptres) suggesting that unmeasured confounders may have attenuated the latter relation. Conversely, using the myopia allele score as the instrumental variable in mendelian randomisation analyses provided little evidence that refractive error affected time spent in education   ; fig 3. , P=0.6) ; fig 3. Mendelian randomisation analyses are based on two pertinent assumptions: the genetic instrumental variables are not associated with any confounders of the exposure-outcome relation, and the genetic instrumental variables are only associated with the outcome through the exposure.In tests of the association between the allele scores for time spent in education and myopia with potential confounders, there was evidence that the geographical coordinate, northing (measured northward distance in UK) was negatively associated with time spent in education  and positively with refractive error . Northing was also associated with the time spent in education (P=7e-5) and myopia (P=6e-3) allele scores (see supplementary table 2). Compared with standard regression, the confounding bias plot suggested that inclusion of the northing variable in the instrumental variable analysis would result in a greater degree of bias for the education allele score but not for the myopia allele score .In contrast, the geographical easting coordinate was positively associated with time spent in education  and negatively associated with refractive error . It was weakly associated with the myopia allele score (P=0.01). However, there was little evidence to suggest a greater degree of bias in the instrumental variable analysis compared with a standard regression with the inclusion of the easting variable . SensitiOne further confounding variable, population stratification principal component 9 (PC9), incurred a greater degree of bias in the instrumental variable regression compared with observational least squares regression. Additional analyses showed that PC9 was associated with a self reported place of birth in Wales (see supplementary figure S2) and also with a −0.17 dioptre  more myopic refractive error, on average (P=4e-3) compared with those who reported being born in England. A mendelian randomisation sensitivity analysis that adjusted for population stratification principal components 1-10 provided similar results to those before adjustment (see supplementary table 4), suggesting that confounding due to PC9 did not lead to appreciable bias.While education legislation has not been different in England and Wales while the UK Biobank participants were in education, Scottish schools normally finish one year earlier and university degrees are correspondingly one year longer. This difference would impact on the years spent in education for Scottish people moving to England to attend university, and vice versa. However, the results of a mendelian randomisation sensitivity analysis restricted to participants born in England were essentially unchanged (see supplementary table 4), providing evidence that imprecision in quantifying years spent in education due to differences in school leaving age did not adversely affect the results.Under the second assumption of mendelian randomisation, genetic variants with pleiotropic effects are invalid instrumental variables. This can be problematic when genetic variants are used without regard for the biological mechanisms through which they affect the exposure—for example, if the genetic variants associated with more years in education also caused myopia independently of the education phenotype. Mendelian randomisation-Egger, weighted mode, and weighted median methods are alternative methods of integrating instrumental variable estimates across individual single nucleotide polymorphisms. These methods allow some of the assumptions of mendelian randomisation to be relaxed providing valid tests for causality despite the presence of invalid instrumental variables .IV=−0.35 dioptres/LOD(education) where LOD is the logarithm of odds for having spent >16 versus ≤16 years in education, 95% confidence interval −0.48 to −0.22), whereas refractive error did not have an effect on time spent in education (βIV=−0.0004 LOD(education)/dioptre, −0.03 to 0.03) (see supplementary table 4).Encoding time spent in education as a dichotomous trait (>16 versus ≤16 years of age when completed full time education) produced the same pattern of causality as the continuous variable, age at which full time education was completed—that is, more time spent in education had an effect on refractive error  with larger standard errors. This was attributable, in part, to the reduced sample size (n=45 535). Again, there was little evidence that refractive error had an effect on time spent in education  (see supplementary table 4).When those who had attended university or college were excluded from the analyses, there was a similar point estimate of the effect of time spent in education on refractive error , with the instrumental variable estimate suggesting a larger negative association . There wIn this study, we found strong evidence that more time spent in education is a causal risk factor for myopia. More specifically, every additional year in education caused an increase in myopic refractive error of −0.27 dioptres/y . Thus the cumulative effect of more years in education on refractive error means that someone attending university would be likely to have at least −1 dioptre more myopia than someone who left school at age 16. A difference of this magnitude would blur vision on a Snellen visual acuity chart to 6/18 and affect the ability to drive without glasses. Those with myopia, by definition, have better near vision than distance vision and require less accommodative effort for near work and study, and so myopia has been proposed as an educational advantage., of which the latter identified people from Wales. Although there are some differences between the education system in England and Wales compared with Scotland, the results held true when analyses were restricted to people from England. Another limitation of this study was selection bias. UK Biobank participants have been shown to be more highly educated, have healthier lifestyles, and have fewer self reported adverse health outcomes than expected compared with the general UK population.Mendelian randomisation is a particularly powerful approach for testing causal hypotheses in epidemiology.When using mendelian randomisation it is not necessary to know how the genetic variants used in the analysis cause the exposure. Yet, without knowing the function of the genetic variants and how they influence the traits described here, it is possible that some single nucleotide polymorphisms may influence the outcome through a pathway that does not involve the exposure—that is, through horizontal pleiotropy. For example, educational outcomes and intelligence are highly correlated, and if intelligence caused myopia through a pathway that did not involve exposure to education, this could cause bias in the mendelian randomisation causal effect estimate (see supplementary figure 3a). In contrast, vertical pleiotropy refers to single nucleotide polymorphisms that influence the outcome through an intermediate phenotype—for example, if some single nucleotide polymorphisms affect exposure to education through their influence on intelligence. Vertical pleiotropy acting through intelligence would not bias the mendelian randomisation causal estimate obtained here (see supplementary figure 3b). Sensitivity analyses  suggested little evidence of unbalanced horizontal pleiotropy in the relation between education and myopia, although such bias cannot be ruled out unequivocally.In agreement with a substantial number of epidemiological studies dating back more than 100 years,www.nhs.uk/conditions/short-sightedness/).Exactly how increasing levels of education cause myopia cannot be inferred from mendelian randomisation analyses, although the known environmental risk factors for myopia provide intriguing clues. Children from developed East and South-East Asian countries consistently report that they spend less time outdoors than children from Australia or the United States,This study provides strong evidence that more time spent in education is a causal risk factor for myopia. With the rapid increase in the global prevalence of myopia and the economic burden of myopia and its vision threatening complications, the findings of this study have important implications for educational practices. Axial eye growth occurs predominantly during the school yearsMyopia, or short-sightedness, is a leading cause of visual disability worldwide, and the global prevalence is increasing rapidly Numerous observational studies have reported strong associations between educational outcomes and myopiaBecause randomising children to different levels of education would be unethical it was not known whether increasing exposure to education causes myopia, myopic children are more studious, or socioeconomic position leads to myopia and higher levels of educationMore time spent in education is a causal risk factor for myopiaThis study highlights a need for further research and discussion about how educational practices might be improved to achieve better outcomes without adversely affecting vision


In recent years, as a secondary analysis in genome-wide association studies (GWASs), conditional and joint multiple-SNP analysis (GCTA-COJO) has been successful in allowing the discovery of additional association signals within detected loci. This suggests that many loci mapped in GWASs harbor more than a single causal variant. In order to interpret the underlying mechanism regulating a complex trait of interest in each discovered locus, researchers must assess the magnitude of allelic heterogeneity within the locus. We developed a penalized selection operator for jointly analyzing multiple variants (SOJO) within each mapped locus on the basis of LASSO (least absolute shrinkage and selection operator) regression derived from summary association statistics. We found that, compared to stepwise conditional multiple-SNP analysis, SOJO provided better sensitivity and specificity in predicting the number of alleles associated with complex traits in each locus. SOJO suggested causal variants potentially missed by GCTA-COJO. Compared to using top variants from genome-wide significant loci in GWAS, using SOJO increased the proportion of variance prediction for height by 65% without additional discovery samples or additional loci in the genome. Our empirical results indicate that human height is not only a highly polygenic trait, but also has high allelic heterogeneity within its established hundreds of loci. Genome-wide association studies (GWASs) have successfully identified many genetic variants that regulate complex traits. However, the associations between a complex trait and genetic variants, such as single-nucleotide polymorphisms (SNPs), are usually very small relative to noise. Thus, GWASs often require large sample sizes to achieve sufficient power, and substantial efforts have been spent on the development of statistical methods to boost GWAS discovery power.Given the legal restrictions on public sharing of individual-level data, it is rarely feasible to pool individual-level data from a number of different cohorts. In spite of this, GWAS summary-level data, in the form of association statistics, are mostly meta-analyzed and reported.In GWASs, if the single most statistically significant variant at a locus is reported, we only capture all the genetic variance—i.e., there is no missing heritability at the locus—when two assumptions hold: (1) there is only one underlying causal variant at the locus, and (2) the causal variant is in complete linkage disequilibrium (LD) with the top variant. However, these two assumptions can both be questioned: (1) there might be multiple causal variants or alleles at the locus so that a single variant cannot account for all the genetic variance at the locus. The phenomenon wherein multiple causal variants or alleles for a particular trait are located at the same locus is known as allelic heterogeneity (AH), whose presence in various complex diseases is reported in a recent study.9However, the forward stepwise selection procedure, such as that implemented in GCTA-COJO, is known to be overly “greedy”; it is prone to eliminating useful predictors that happen to be correlated with selected predictors.There is theoretical and empirical evidence that simultaneous modeling of multiple predictors with penalization provides a better variable selection procedure than the forward stepwise selection.The aim of this study is to develop, implement, and validate LASSO by using GWAS summary statistics (SOJO) for genomic loci discovered in standard GWASs. First, we show that using summary-level data for LASSO achieves results that are approximately equivalent to those obtained when LASSO is based on individual-level data. We then provide simulation studies to show how SOJO can outperform GCTA-COJO in finding additional association signals in loci with different LD structures. We applied SOJO on GWAS summary-level data of three anthropometric traits—height, body mass index (BMI), and waist-to-hip ratio after adjustment for body mass index (WHRadjBMI) reported by the GIANT consortium—and validated the out-of-sample predictive performance in the large national cohort UK Biobank (UKB). By implementing SOJO, we have added additional association information to the results of standard GWASs and GCTA-COJO analyses, improved out-of-sample predictive heritability, and revealed different levels of allelic heterogeneity for different traits. The SOJO analysis is implemented in our free and open-source R package.y is potentially affected by a group of genetic variants n individuals, then In this section, we describe how to achieve LASSO estimates by using summary-level statistics from a GWAS meta-analysis and a reference sample. Assume a quantitative trait The regularization pathThe first step is to get the covariance structure between variants and the trait. To simplify the formulae, we center the data so that j isBased on gression  and σ2 ij isbˆj= including both of them didn’t significantly increase the amount of information gained, and (2) including both might have generated numerical errors when the tuning parameter went to zero and the model approached the standard multiple regression.p predictors, one can say their model complexity is the same because their degrees of freedom are both equal to p. However, when it comes to evaluating two complex variable selection procedures, especially when comparisons or shrinkage is involved, the degrees of freedom or the complexity of the model might no longer be equal to the number of variables selected by the model.For the comparison between SOJO and GCTA-COJO to be fair, the two must be under the same level of model complexity. Degrees of freedom is often used as a measurement of model complexity. When comparing two linear models, both with For a function k variables in our model, SOJO costs exactly k GDF, which is consistent with theoretical results, whereas GCTA-COJO usually costs more than k GDF.Estimating GDF for GCTA-COJO and SOJO with a Monte Carlo methodWe can approximate the LASSO result at any tuning parameter by using (1) the covariance structure between variants and the trait and (2) the LD structure between variants. The former covariance structure can be estimated from GWAS meta-analysis summary-level data, and the LD structure can be estimated from a reference sample, such as a subcohort of the GWAS meta-analysis. We simulated a model of two correlated causal variants in order to compare SOJO and GCTA-COJO in terms of sensitivity and specificity. The area under the curve (AUC) of SOJO is larger than that of GCTA-COJO in most cases . The onlGIANT: the Swedish Twin Registry  as our reference sample and focused on the 644,556 chip variants in TwinGene. Using GIANT summary statistics for height, BMI, and WHRadjBMI of 253,288, 322,154, and 210,088 individuals, and data for 120,286 individuals from UKB as a validation sample, we prioritized 8,470, 1,026, and 522 jointly associated variants by implementing SOJO on 423, 77, and 49 established loci for the three traits, respectively  and 0.62 (p = 2.3 × 10−44). In terms of choosing a proper threshold for GCTA-COJO, a strict threshold will make LASSO results dominate the ratio, whereas a loose threshold will generate lots of noise (−4), i.e., for a locus that has 0.1% more regional In principle, if GCTA-COJO does not miss any causal variant, and if we perform LASSO for each locus by using cross-validation and set a fixed p value threshold, e.g., of noise . In our ional h2  (slope oional h2  and S5.FWe introduced a selection operator, SOJO, that analyzes multi-variant summary association statistics and is based on approximate LASSO shrinkage estimators. SOJO is more powerful than conditional and joint analysis in GCTA in terms of both discovery and prediction. SOJO is computationally fast because it is based on GWAS meta-analysis summary statistics and LD structure estimated from a reference cohort . The smaAs in GCTA-COJO, the reference sample is assumed to be from the same population where the meta-analysis sample is from. Therefore, a subcohort involved in the meta-analysis is usually valid as a reference sample. However, an outside sample can also be a reference sample if it well represents the population of interest. The sample size of the reference sample should be large enough so that the LD correlations can be estimated accurately. According to a simulation result by Yang et al.,In many regions, SOJO top variants were also selected by GCTA-COJO . This isEvidence shows that jointly analyzing multiple correlated traits can improve both discovery powerHere, we use UKB, an independent individual-level data sample, as the validation sample to determine a proper amount of regularization or a reasonable number of variants selected for each locus. If there is no available independent sample, we suggest the use of the reference sample as the validation sample. Although the reference sample is used for estimating LD structure and was included in the GWAS meta-analysis where the summary statistics were from, it can still function as a validation sample because it usually contributes only a little to the estimation of genetic effects. Our method can also be used directly with individual-level data where the reference sample is the whole cohort. In this case, SOJO is equivalent to standard LASSO that is based on individual-level data. If the summary statistics and LD structure have been computed and stored beforehand, SOJO is computationally faster than standard LASSO. Another benefit of SOJO is its ability to handle variants with unequal sample size. This means that when individuals or individual cohorts have missing genotype data, SOJO is able to take this into account to estimate correlations between the variants and the trait instead of removing valuable individuals because of missing data.According to our empirical results, human height not only is a highly polygenic trait but also has high allelic heterogeneity. This interesting coincidence might be due to assortative mating; i.e., individuals prefer partners with similar phenotypes.The tuning parameter in LASSO is usually chosen by cross-validation, which is impossible for SOJO because the individual-level data of the GWAS meta-analysis are absent. Variant selection based on one validation sample might be less stable than standard cross-validation. Hence, SOJO could be improved by using the validation sample more thoroughly via splitting or bootstrapping. If one would like to avoid using the validation sample, but use only GWAS summary statistics and the reference sample, some additional methods are worthy of investigation. Although the individual-level data of the GWAS meta-analysis is absent, making it impossible to bootstrap the individuals, one could perform a parametric Monte Carlo simulation on the estimated genetic effects, given that their point estimates and standard errors are available from summary association statistics and their correlations can be estimated from the reference sample. With Monte Carlo simulation results, we can improve the variant detection and phenotypic prediction of SOJO further by implementing bootstrap-based methods such as stability selection


QFN.wsu loci were detected in multiple environments, whereas six of the 34 QPHS.wsu loci were detected in two of the five environments. There was no overlap between the QTN detected based on FN and PHS, and there was little correlation between the two traits. However, both traits appear to be PHS-related since 19 of the 34 QPHS.wsu loci and four of the nine QFN.wsu loci co-localized with previously published dormancy and PHS QTL. Identification of these loci will lead to a better understanding of the genetic architecture of PHS and will help with the future development of genomic selection models.Preharvest sprouting (PHS), the germination of grain on the mother plant under cool and wet conditions, is a recurring problem for wheat farmers worldwide. α-amylase enzyme produced during PHS degrades starch resulting in baked good with poor end-use quality. The Hagberg-Perten Falling Number (FN) test is used to measure this problem in the wheat industry, and determines how much a farmer's wheat is discounted for PHS damage. PHS tolerance is associated with higher grain dormancy. Thus, breeding programs use germination-based assays such as the spike-wetting test to measure PHS susceptibility. Association mapping identified loci associated with PHS tolerance in U.S. Pacific Northwest germplasm based both on FN and on spike-wetting test data. The study was performed using a panel of 469 white winter wheat cultivars and elite breeding lines grown in six Washington state environments, and genotyped for 15,229 polymorphic markers using the 90k SNP Illumina iSelect array. Marker-trait associations were identified using the FarmCPU R package. Principal component analysis was directly and a kinship matrix was indirectly used to account for population structure. Nine loci were associated with FN and 34 loci associated with PHS based on sprouting scores. None of the  Triticum aestivum L.), barley (Hordeum vulgare L.), and sorghum (Sorghum bicolor)  test Perten, . During Here we present a genome-wide association mapping study (GWAS) for PHS tolerance in white wheat based on sprouting scores and FN. A large panel of 469 white wheat lines representing six northwestern U.S. breeding programs was examined over multiple environments in order to characterize the genetic architecture of PHS tolerance/susceptibility. The goal was to identify quantitative trait nucleotides (QTN) associated with PHS tolerance in white wheat breeding programs, while examining the phenotypic connection between FN and spike-wetting test scores.T. aestivum ssp compactum) genotypes with compact spike morphology and 64% soft white genotypes with lax spike morphology. The same panel was recently analyzed for soil acidity, aluminum tolerance, Cephalosporium stripe resistance, and stripe rust resistance  using recommended agronomic practices for those locations. The panel was also grown as headrows in Pullman, WA in 2013 (P13). Heading dates from the Pullman 2014 environment were determined after 50% of the plot reached full spike emergence from the boot. Table The mapping panel was grown as 1.5 m long headrows at Central Ferry, WA in 2014, 2015, and 2016 , or as 8 mReduced FN was examined in field-grown material after PHS induced either by natural or artificial rain events. PHS-inducing natural rain events occurred after physiological maturity in Pullman 2013 and Central Ferry 2016. Therefore, these two environments were not used for spike-wetting tests, since the material was already sprouted. In Pullman 2013, rain occurred over 3 consecutive days with precipitation amounts of 0.38, 0.025, and 0.025 cm, and high temperatures of 22.8, 18.2, and 23.8°C, respectively /(7 × n) where s is the sprouting score on each day and n is the maximum sprouting score. SI ranged from 0 to 1, where an SI of 1 indicated that the spike reached 100% highly sprouted by day 1 of misting. For the day 3, 4, 5, 6, and 7 sprouting scores and for the SI of each accession, best linear unbiased predictors (BLUPs) were calculated within each environment over the five technical replicates using the MIXED procedure in SAS/STAT v9.4  was calculated as , rather than the heritability (H2), was calculated using the lme4 package v1.1-13 in R . Missing values for markers with published locations were imputed using default parameters in BEAGLE v3.3.2  > 6.55).FarmCPU default parameters were used except that the “optimum” bin method with default range and interval parameters was used instead of the “static” method. The FN trait least squares means (LSMeans) and the sprouting score BLUPs were used as dependent variables in this GWAS , chromosome location (cM) based on Wang et al. (r2); (b) allelic effect; and (c) marker p value.Linkage disequilibrium (LD) was calculated using JMP software v6.0 . LD of significant markers were used to estimate boundaries of potential quantitative trait loci (QTL) using the criteria of LD  was greater than sprouting scores (R2 < 0.31), especially when covariates like operator, machine, subset, and replicate, were taken into account . The genotypic repeatability of sprouting was highest when spikes were misted longer or when all measurements were integrated in the SI  = 5.88) and 7A (–log10(p) = 6. 17) in Central Ferry 2014 were just below the stringent threshold for significance (–log10(p) = 6. 55). QFN.wsu-7A.1 and QFN.wsu-7B.2 had the largest effects, increasing FN by 26 and 27 s, respectively. QFN.wsu-7A.2 had the highest significance (–log10(p) = 12.36) and had an 8 s effect. In order to reduce the effect of loci unrelated to PHS tolerance on the GWAS, the data were re-analyzed with 400 s set as the maximum possible FN. When this was done, none of the nine QFN.wsu were detected and two unique significant QTN, QFN.wsu-6A and QFN.wsu-7A.3 were identified in Central Ferry 2016  , whereas days 4, 5, 6, and SI did not  Figure . Seven QI Figure . An assoe Figure . The QPHs Figure . No QPHSper se, the GWAS was repeated with the maximum sprouting score set at 5 and referred to as QPHSg.wsu  < 37.13), and had strong effects (0.02 to 0.72).In order to reduce the effect of post-germinative growth versus germination QPHS.wsu-2D locus was near the C locus region for compact spike morphology, we examined whether the club wheat breeding program contributed more PHS tolerance to the GWAS than the lax wheat breeding programs  of up to 30.03 and an effect of 1.08. An additional 32 QPHSnPC.wsu and 2 QFNnPC.wsu were detected, whereas 15 QPHS.wsu and 2 QFN.wsu were found in common . The number of QPHS.wsu loci varied more widely within the accessions (8 to 26), making it easier to assess the effects of pyramiding multiple tolerance loci  and FN (QFN.wsu). FN is an important and complex trait that determines the value of the grain in the wheat industry. While there were 34 significant QPHS.wsu loci across the five different sprouting time points and sprouting index, only nine significant QFN.wsu loci were identified. We expected FN and sprouting scores to identify some of the same QTN because the α-amylase expression that lowers FN is a consequence of germination. However, none of the identified significant FN and PHS loci were linked (Table QFN.wsu-4A and QPHS.wsu-4A.3 appeared to be close to one another (1 cM apart), they were not in the same linkage group (p between 0.05 and 0.01), and had only a −0.13 correlation to one another. Moreover, we failed to find a strong correlation between FN and sprouting scores. This result contrasts with previous studies showing a correlation of up to −0.8 between spike-wetting tests and FN in Canadian and Chilean breeding lines  were near published QTL , identified by map-based cloning in both Japanese and U.S. wheat  gene likely accounts for the seed dormancy providing PHS tolerance on chromosome 4A. Future work will need to examine if the PHS tolerance loci mapped in the current study are associated with the known dormancy-associated polymorphisms in TaMFT and TaMKK3. If so, then these perfect markers can be used for selecting PHS tolerance within the breeding programs represented in this GWAS. Identifying QTL near regions of known PHS QTL validates the GWAS and suggests that breeding programs in the northwestern U.S. have historically used multiple sources of PHS tolerance.Many e Figure . QPHS.wsQPHS.wsu-2D locus co-localized both with a known PHS locus and with the C locus that determines club head type , and there were two PHS susceptible club wheat lines (J970057-5 and ARS00226) that did not carry the QPHS.wsu-2D locus. While these counter-examples suggest that there was a PHS QTL strongly linked to the C locus, they are not proof because these PHS phenotypes may have resulted from variation at other loci. Future work will need to examine this question using near-isogenic lines that differ only for the C locus and for the QPHS.wsu-2D locus.The strong QPHS.wsu loci correlated to increasing sprouting index and sprouting scores, we observed little or no correlation to increasing FN in natural rain, artificial rain, or no-rain environments  of FN increased when we took experimental covariates (such as machine and operator) and technical replicates into account (Table r > 0.80), it had fewer samples below 300 s suggesting that less sprouting occurred in their environments. Breeders cannot rely on natural rain occurring when they want to screen for low FN due to PHS, making the use of artificial rain necessary. Other differences in the environment, such as temperature during maturation or temperature during the sprout-inducing rainfall, can impact grain dormancy, PHS susceptibility, and FN. Future artificial rain experiments may be improved by applying the artificial rain during lower evening temperatures or letting the wheat after-ripen longer in the field prior to misting.Breeding for FN is complicated by the fact that it is a complex trait governed by multiple factors. Although the intention was to map preharvest sprouting QTL, our FN field environments may have also experienced conditions that induced late maturity α-amylase (LMA). During LMA, α-amylase is induced in response to large temperature fluctuations during late grain filling (Farrell and Kettlewell, L Figure . In the L Figure . Such prnt Table . The FN nt Table . Environnt Table . While tnt Table  study haThe spike-wetting test has long been favored for selecting preharvest sprouting tolerance because the experimental design takes into account after-ripening time, spike morphology, and grain dormancy/germinability (Paterson et al., Seed dormancy and PHS tolerance are stronger if temperatures are cool during grain maturation (Nakamura et al., QPHS.wsu were identified in at least two of the five environments. In fact, the correlations between our environments were as good as those in other spike-wetting test studies (Jaiswal et al., PHS tolerance is profoundly impacted by environmental conditions during grain maturation and during the sprout-inducing rain event (Cao et al., SM, KC, and CS: Designed the experiments; SM: Conducted the experiments, analyzed the phenotypic data, performed the statistical analysis and GWAS, and constructed the visualizations; JG: Curated and filtered the genotypic data and performed the LD analysis; MH: Calculated the phenotypic variation; MH and ZZ: Provided expert guidance on performing the GWAS; KC and AC: Provided field resources; CS, KC, AC, and ZZ: Obtained funding; SM and CS: Wrote the manuscript.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Neisseria meningitidis illustrate the versatility and potential of our method, confirming previously-identified penicillin resistance loci and resulting in the identification of both well-characterised and novel drivers of invasive disease. Our method is implemented as an open-source R package called treeWAS which is freely available at https://github.com/caitiecollins/treeWAS.Genome-Wide Association Studies (GWAS) in microbial organisms have the potential to vastly improve the way we understand, manage, and treat infectious diseases. Yet, microbial GWAS methods established thus far remain insufficiently able to capitalise on the growing wealth of bacterial and viral genetic sequence data. Facing clonal population structure and homologous recombination, existing GWAS methods struggle to achieve both the precision necessary to reject spurious findings and the power required to detect associations in microbes. In this paper, we introduce a novel phylogenetic approach that has been tailor-made for microbial GWAS, which is applicable to organisms ranging from purely clonal to frequently recombining, and to both binary and continuous phenotypes. Our approach is robust to the confounding effects of both population structure and recombination, while maintaining high statistical power to detect associations. Thorough testing via application to simulated data provides strong support for the power and specificity of our approach and demonstrates the advantages offered over alternative cluster-based and dimension-reduction methods. Two applications to  N. meningitidis. We have developed an easy-to-use implementation of treeWAS in the R environment, which should be useful to a wide range of researchers in microbial genomics.Measurable differences often exist within a microbial population, with important ecological or epidemiological consequences. Examples include differences in growth rates, host range, transmissibility, antimicrobial resistance, virulence, etc. Understanding the genetic factors involved in these phenotypic properties is a crucial aim in microbial genomics. A fundamental approach for doing so is to perform a Genome-Wide Association Study (GWAS), where genomes are compared to search for genetic markers systematically correlated with the property of interest. If this strategy were implemented naively in microbes, it could lead to spurious results due to the confounding effects of population structure and recombination. Here we present treeWAS, a new phylogenetic method to perform microbial GWAS that avoids these pitfalls. We show, using simulated datasets, that treeWAS is able to distinguish between genetic markers that are truly associated with the property of interest and those that are not. Furthermore, we demonstrate that treeWAS offers advantages in both sensitivity and specificity over alternative cluster-based and dimension-reduction techniques. We also showcase treeWAS in two applications to real datasets from  This is a PLoS Computational Biology Methods paper.Owing to rapid progress in sequencing technologies, the accumulation of microbial genome sequences has begun to outpace the development of statistical and computational tools for their analysis. As a result, opportunities to reduce the global burden of infectious disease are missed. Meanwhile, infectious diseases remain accountable for 15% of worldwide annual mortality –5. DiscoGenome-wide association studies (GWAS) can be used to make these inferences, linking genotype to phenotype by testing for statistical associations between the two. GWAS have become a tool of choice in human genetics, since the publication of the first such studies in the early 2000s –9, leadiThe purpose of GWAS is to identify statistically significant associations that may indicate the presence of a causal relationship between genotype and phenotype while rejecting spurious associations arising from confounding factors. In microbes, smaller genome sizes and the ability to manipulate these genomes in the laboratory may improve the power and computational ease of GWAS and facilitate the confirmation of candidate loci . On the Most microbial GWAS analyses to date have made an effort to control for the confounding potential of population structure. The strength of this confounding effect increases both with the degree to which allele frequencies differ between subpopulations in a sample and the extent to which phenotypic states cluster within these lineages or clades , 19. CluFortunately, clonality also enables the adoption of a phylogenetic solution –33. PhylNeisseria meningitidis. First, we investigate penicillin resistance and demonstrate that our approach can confirm known resistance loci. Second, we examine invasive disease, which reveals both previously characterised and novel invasiveness factors and illustrates the ability of our methodology to identify associations when applied to complex phenotypes.Here we propose a new phylogenetic approach to GWAS called treeWAS that is able to overcome many of the limitations of existing microbial GWAS approaches. Within our analytical pipeline, data simulation based on parameters of the empirical dataset under analysis allows us to account for the composition of the genetic dataset, the population structure of the sample, and the confounding effects of recombination. We apply multiple complementary scores of association to enhance statistical power and improve detection of associations underlying subtle and complex phenotypes, such as host association or invasiveness. Below, we present the results of rigorous testing on simulated datasets, and compare performance with alternative approaches, including cluster-based and dimension-reduction methods. We also demonstrate how treeWAS responds to varying levels of recombination and contrast this to previous methods. We show that treeWAS provides both specificity and power in a wide range of settings, and consistently offers the best overall performance. Finally, we present two applications to real data from Our central aim is to delineate true signals of association from a noisy background of spurious associations. To accomplish this, our method uses the simulation of a null genetic dataset to establish whether high association score values in the empirical dataset under analysis are likely to be truly significant or may, in fact, arise by chance as a result of confounding factors found in the empirical dataset. Outside of the GWAS literature, similar approaches comparing null and empirical distributions have been used to determine whether inferred ancestry supports the functional linkage of genes , 36. In The treeWAS approach is implemented in the following steps:Phylogenetic reconstruction can be performed within treeWAS by distance-based [ce-based –40 or mace-based  methods.ce-based , 42, 43.Computation of the homoplasy distribution, containing site-specific numbers of substitutions drawn from the empirical dataset, is performed with the Fitch parsimony algorithm [lgorithm .Simulation of null genetic data enables the delineation of true associations from spurious associations. We compare the relationships between genotype and phenotype at all loci in the real data to those in a simulated dataset that embodies only potentially confounding factors. Simulation of this “null” genetic dataset is guided by three parameters: (i) the phylogenetic tree, (ii) the homoplasy distribution, (iii) the number of loci to be simulated, Nsim, which is recommended to be at least ten times the number of biallelic sites in the empirical dataset. Each of the Nsim loci is simulated along the phylogenetic tree, from root to tips, undergoing a number of substitutions drawn from the homoplasy distribution on branches selected randomly with probabilities proportional to branch length. The original phenotype is maintained across the leaves. By retaining the phylogenetic tree and the distribution of phenotypic states, but reassigning substitutions to new branches, we are able to produce a simulated dataset that resembles the empirical dataset in population structure and genetic composition, including the effects of mutation and recombination. Associations due to confounding factors, but no true associations with the phenotype, are thus recreated by the simulation process.Ancestral character estimation is required prior to association testing. A marginal reconstruction of the ancestral states of both genotype and phenotype must be performed via parsimony [arsimony  or ML [4arsimony , 47 . Associations between simulated loci and the empirical phenotype are first measured, allowing for the identification of a null distribution of association score statistics under the null hypothesis of no association. Associations between empirical loci and the phenotype are then measured and evaluated with reference to this null distribution.Identification of significance threshold and associations proceeds by drawing a threshold in the upper tail of the null distribution, at the value corresponding to a base p-value  that has been corrected for multiple testing to account for both the number of genetic loci and the three association tests . Among the set of empirical association scores, all values that exceed this threshold are deemed to be statistically significant associations and, thus, candidates for true biological association, pending subsequent confirmatory analyses.i, respectively. i. n and nb denote respectively the number of leaves and branches on the phylogenetic tree.The design of treeWAS, particularly its use of the null distribution, enables strict control over the false positive rate. This presents the opportunity for power to be augmented by applying multiple independent tests of association. We therefore measure the association between each genetic locus and the phenotype with three separate tests, described below and illustrated in Score 1, the “Terminal Score”, measures sample-wide association across the leaves of the phylogenetic tree. For a binary phenotype, this score is equivalent to counting the four terminal state combinations, with and without the phenotype, and with and without the genotype, as previously proposed [proposed . GeneralScore 2, the “Simultaneous Score”, measures the degree of parallel change in the phenotype and genotype across branches of the tree. For a binary phenotype with a parsimonious ancestral state reconstruction, as in Score 3, the “Subsequent Score”, measures the proportion of the tree in which the genotype and phenotype co-exist. It is the mathematical solution to the integral of an association score along all points of the phylogenetic tree  between an ancestral node (in the rows) and a descendant node (in the columns):Q matrix is parameterised by s, which controls the baseline substitution rate and applies to all columns, and a, an association factor that establishes the preference for one form of association  over the opposite . The parameter s is divided by the sum of the branch lengths before building Q. In all simulations, initial parameters were set to s = 20 and a = 10. To identify the probabilities of transition for a branch of length l, the instantaneous transition rate matrix, Q, is converted into a matrix of probabilities, P = exp(Ql), via matrix exponentiation, which takes into account the length l of the branch in question.Each simulated dataset contained 100 individuals and 10,000 binary loci, of which ten loci were associated with a binary phenotype. Variation in the background recombination rate, the ancestral relationships between genomes, the degree of phenotypic clustering among related isolates, and the effect size of associations added complexity and noise to the simulated data and increased the challenge of association testing for treeWAS and all comparator methods. The non-associated loci were simulated using homoplasy distributions corresponding to four recombination rates  see . Geneticχ2 test available in PLINK version 1.07 [χ2 test with Genomic Control (GC), has been used in bacterial GWAS [χ2 test [K population clusters by adopting a stratified 2x2xK design and has been used in bacterial GWAS [To each of the simulated datasets, in addition to treeWAS, we applied six alternative GWAS methods. The Fisher’s exact test, and the ion 1.07  were useial GWAS  and provial GWAS , 22. PCAial GWAS , 50 and ial GWAS –28. We f[χ2 test . The Coc[χ2 test ) provideial GWAS , 23, 24.The performance on simulated datasets was evaluated along four metrics: the False Positive Rate (FPR), Sensitivity, Positive Predictive Value (PPV), the proportion of results that are true positives, and the F1 Score, which is the harmonic mean of Sensitivity and PPV . Our appIn addition to providing a thorough control over population structure, treeWAS was able to account explicitly for the varying confounding effect of recombination. In the simulated datasets analysed above, the phenotype and associated loci underwent between four and 23 binary state substitutions as a result of the probabilistic simulation process, with an average of 14 substitutions per tree. As such, the probability of chance correlation with the resulting pattern of phenotypic clustering increased as the number of substitutions among non-associated loci was elevated to similar levels by recombination see . Fig 3A Having described the performance of treeWAS on simulated data, we now compare it with the performance of alternative methods. All of the non-phylogenetic approaches to correcting for population structure inherently simplify the extensive genetic relationships between isolates. The k-means clusters used in the CMH test, and the principal components of PCA and DAPC have been previously shown to correspond to the major clades and genealogical divisions of a phylogenetic tree , 28, 53.Building on the foundation of low FPR, treeWAS is able to enhance power by drawing on the cumulative findings of multiple tests of association. The non-phylogenetic alternatives, by contrast, face an inherent trade-off between sensitivity and specificity. The CMH test more effectively managed the sensitivity-specificity trade-off by applying a more conservative stratified test of association to the genetic data matrix without regressing out any relevant information. In fact, we see from Additionally, Overall, the comparison of methods in Figs N. meningitidis isolates with a penicillin resistance phenotype. We used the Neisseria Bacterial Isolate Genome Sequence Database  to downup B see , extractr pylori . Becauser pylori . treeWASThe penicillin resistance phenotype was analysed in two ways: as a binary and as a continuous variable. The binary phenotype was categorised according to the penicillin minimum inhibitory concentration (MIC), defining susceptible as MIC ≤ 0.06 and resistant as MIC > 0.06. The continuous phenotype was defined as the ranks of the MIC values, rather than the MIC values themselves, whose distribution was highly skewed and which were less informative than the relative MIC values.penA) gene, encoding penicillin-binding protein 2  are produced [penA, arise via homologous recombination [penA sequences among susceptible isolates [Analysis of the accessory gene presence or absence data did not result in the identification of any gene significantly associated with either the binary or continuous penicillin resistance phenotype. However, application of treeWAS to the set of core SNPs led to the identification of many significant loci. Analysis of the binary penicillin resistance phenotype resulted in the identification of 162 significant SNPs, all of which were located in the well-characterised NEIS1753  has well-characterised roles in virulence, enabling adhesion, colonisation, and invasion of mucosal cells [MafA2, another adhesin, plays a similar role in pathogenic Neisseria [hmbR, to invasive disease in N. meningitidis [hmbR may be a good target for vaccine development [In the analysis of the accessory gene presence or absence data, treeWAS identified 12 genes associated with carriage or invasiveness , Table 1al cells , 65. Mafeisseria , 67. Epingitidis , 69. Morelopment .N. meningitidis that enables immune evasion via surface modulation, and favours colonisation and survival in the nasopharyngeal niche [We also identified nine genes whose presence was associated with Neisserial carriage. These included the cell-surface protein encoded by NEIS0956 and the DNA transport competence proteins encoded by NEIS1574, NEIS1880, and NEIS1996, which enable genetic transformation , 72. Theal niche . This reporA gene is well known for encoding a surface protein that drives hyperinvasivity in N. meningitidis [gapA-2 may facilitate the adhesion to and invasion of host tissues [N. meningitidis is not yet fully understood, we anticipate that future work will elucidate the roles of other loci in In the analysis of core SNPs, treeWAS identified seven associated loci , Table 2ngitidis –78. Like tissues . As the N. meningitidis. Subsequent analyses in the laboratory would be required to confirm that a true biological or causal relationship accompanies this statistical significance.Overall, treeWAS was able to identify both previously-known and putatively novel genes and SNPs in significant association with the commensal or invasive phenotype in https://github.com/caitiecollins/treeWAS.Microbial GWAS has the potential to reveal many important features of microbial genomes. Application has however been so far hampered by a lack of well founded and thoroughly tested methodology. Here we proposed a new phylogenetic approach to microbial GWAS that is able to control for the disruptive effects of both population structure and recombination, whilst still retaining a high statistical power to detect real associations. Application to both simulated and real datasets demonstrated that our method is accurate, efficient and versatile, being able to detect associations in both the core and pan-genome and for both categorical and continuous phenotypic measurements. We have implemented our approach in a user-friendly R package, treeWAS, which is freely available for public use at S1 Appendix(PDF)Click here for additional data file.S2 Appendix(PDF)Click here for additional data file.S3 Appendix(PDF)Click here for additional data file.S4 Appendix(PDF)Click here for additional data file.S5 Appendix(PDF)Click here for additional data file.S6 Appendix(PDF)Click here for additional data file.S7 Appendix(PDF)Click here for additional data file.S8 Appendix(PDF)Click here for additional data file.S9 Appendix(PDF)Click here for additional data file.S1 FigA: At left, the clonal genealogy reconstructed with ClonalFrameML, and terminal phenotype . At right, an alignment of the 67 unique SNPs column patterns  that were observed among the 140 significant SNPs. B-D: Null distributions of simulated association scores for (B) Score 1, (C) Score 2, (D) Score 3, a significance threshold (red), above which real associated SNPs are indicated. E-G: Manhattan plots for (E) Score 1, (F) Score 2, (G) Score 3 showing association score values for all SNPs, a significance threshold (red), above which points indicate significant associations.treeWAS identified 140 SNPs associated with penicillin resistance. (PDF)Click here for additional data file.S2 FigA: At left, the clonal genealogy reconstructed with ClonalFrameML, and terminal phenotype . At right, an alignment of the 30 significant SNPs . B-D: Null distributions of simulated association scores for (B) Score 1, (C) Score 2, (D) Score 3, a significance threshold (red), above which real associated SNPs are indicated. E-G: Manhattan plots for (E) Score 1, (F) Score 2, (G) Score 3 showing association score values for all SNPs, a significance threshold (red), above which points indicate significant associations.treeWAS identified 30 SNPs associated with the ranked penicillin MIC values. (PDF)Click here for additional data file.S1 File(XLS)Click here for additional data file.S2 FileNeisseria meningitidis whole-genome sequences.These loci were identified as significantly associated with the continuous ranked penicillin MIC phenotype, when treeWAS was applied to a dataset of 171 core SNPs extracted from serogroup B (XLS)Click here for additional data file.S3 File(XLS)Click here for additional data file.S4 Fileversus susceptible (MIC > 0.06), when treeWAS was applied to a dataset of 171 core SNPs extracted from serogroup B Neisseria meningitidis whole-genome sequences.These loci were identified as significantly associated with the binary penicillin resistance phenotype, resistant (MIC < = 0.06) (XLS)Click here for additional data file.


The aim of the this study was to identify SNP markers associated with five important wheat quality traits , and to investigate the predictive abilities of GBLUP and Bayesian Power Lasso models for genomic prediction of these traits. In total, 635 winter wheat lines from two breeding cycles in the Danish plant breeding company Nordic Seed A/S were phenotyped for the quality traits and genotyped for 10,802 SNPs. GWAS were performed using single marker regression and Bayesian Power Lasso models. SNPs with large effects on Zeleny sedimentation were found on chromosome 1B, 1D, and 5D. However, GWAS failed to identify single SNPs with significant effects on the other traits, indicating that these traits were controlled by many QTL with small effects. The predictive abilities of the models for genomic prediction were studied using different cross-validation strategies. Leave-One-Out cross-validations resulted in correlations between observed phenotypes corrected for fixed effects and genomic estimated breeding values of 0.50 for grain protein content, 0.66 for thousand-kernel weight, 0.70 for falling number, 0.71 for test weight, and 0.79 for Zeleny sedimentation. Alternative cross-validations showed that the genetic relationship between lines in training and validation sets had a bigger impact on predictive abilities than the number of lines included in the training set. Using Bayesian Power Lasso instead of GBLUP models, gave similar or slightly higher predictive abilities. Genomic prediction based on all SNPs was more effective than prediction based on few associated SNPs. Triticum aestivum L.) is a major cereal crop that is grown in most parts of the world. In 2014, more than 700 million tons of wheat was produced globally  gene at the same locus and by minor QTL (Quantitative Trait Loci) on other chromosomes. Deletions or knock-out mutations in either of the Pin genes lead to increased hardness  is a grain quality trait that is important to many end-users  models are commonly used for genomic selection. In these multiple regression models, a high number of SNP effects are fitted simultaneously  of the Danish plant breeding company Nordic Seed A/S were used for the analyses. The lines of the first breeding cycle, set2014, consisted of 321 lines and were harvested in 2014, and the lines of the second breeding cycle, set2015, consisted of 314 lines that were harvested in 2015. In total, 96 different lines were used as crossing parents in the two sets, and 6 of these lines were used as parents in both sets. The number of different full-sib families from the crosses was 159, and the number of lines in each full-sib family ranged from 1 to 33 with an average of 10 lines , wi is the vector of genotypes of the ith SNP coded as 1, 0, −1, ai is the additive genetic effect of the ith SNP, u is a vector of additive genetic effects of the lines [u ~ N, where G is a G-matrix and e is a vector of random residual effects , where I is an identity matrix and σe2 is the residual variance). The effects of year and set (breeding cycle) could not be separated, since each line was only tested 1 year. Software package DMU was used for estimation of model effects and variance components by restricted maximum likelihood , and P is a matrix with MAF calculated as 2(pi – 0.5).where Population structure was studied by performing a principal component analysis on the G-matrix computed from all 10,802 SNPs using the built-in R function “prcomp” .Genomic inflation factors, λGWAS were also performed by fitting all SNPs at the same time with a Bayesian Power Lasso model using the Bayz software Janss, :y is a vector of observed phenotypes, b is a vector of the mean + year/set effect with design matrix X, Z3 is a matrix of the alleles of the SNPs coded as 0, 1, 2, u is a vector of additive genetic SNP effects, and e is a vector of residual effects. Residuals were assigned a Normal prior distribution. The residual variance, the mean, year/set effect, and rate parameter, λRP, were assigned flat prior distributions. The prior distribution of SNP effects was assigned to be an exponential power distribution:where m is number of markers and β is shape parameter to control the sparsity, which affects the shrinkage of the SNP effects. When β is set to 1, the model is equivalent to the standard Bayesian Lasso, where the absolute SNP effects, |ui|, are assumed to follow an exponential distribution. In this case, large effects are shrunken a bit less and small effects are shrunken a bit more than in the Normal distribution. Setting β to less than 1, increases the difference between markers with large and small effects even further, as it is |ui|β that follow an exponential distribution  and using a GBLUP model:y is a vector of observed phenotypes, X and Z4 are design matrices, b is a vector of fixed effect (mean and year/set), u is a vector of additive genetic effects , where G is a G-matrix computed as above (2) using all 10,802 SNPs and e is a vector of random residual effects ).where Estimation of model effects and variance components for the GBLUP and Bayesian Power Lasso models were done using DMU and Bayz, respectively. For the GBLUP models, the narrow sense genomic heritability  is the average diagonal element of the G-matrix , where h2 was calculated by dividing the additive genetic variance (variance of GEBVs) with the phenotypic variance.For the Bayesian Power Lasso models, Predictive abilities of the models were determined as the correlations between observed phenotypes corrected for fixed effects and GEBVs. These correlations were compared with the square root of the narrow sense genomic heritability, which is the maximum correlation that can be achieved. Bias in the genomic predictions was calculated as the slope of the regression line of the corrected phenotypes on the GEBVs. The expectation of this slope is 1.0, and the bias is the deviation from this expectation.Several types of cross-validation strategies were tested to study the effectiveness of different approaches for implementation of genomic selection in breeding programs:- LOO (Leave-One-Out), where the GEBV of each line was predicted based on the rest of the lines. The LOO strategy was used to study the predictive ability when using the largest training set available and the highest possible genetic relationship between lines in the training and validation set.- LFO (Leave-Family-Out), where the GEBVs of lines in each half-sib family were predicted based on lines from other half-sib families, so that they had no parents in common. The LFO cross-validation strategy was used to study the effect of the genetic relationship between the lines in training and validation sets.- LSO (Leave-Set-Out), where the GEBVs of lines in each set were predicted based on lines only from the other set. The LSO cross-validation strategy was used to study the predictive ability when predicting GEBVs of lines from one breeding cycle based on lines from another breeding cycle.- k-fold, where the lines were randomly divided into k folds  of equal size and the GEBVs of lines in each fold were predicted based on lines only in the other folds. The size of the training sets in the 2-, 5-, and 10-fold cross-validations were approximately 318 lines, 508 lines, and 572 lines, respectively. The k-fold cross-validation strategy was used to study the effect of the size of the training set.Predictions of breeding values were also performed using the three and the ten best SNPs for each trait according to the single marker GWAS or the Bayesian Power Lasso (model 1 or 3). Here, the 635 lines were randomly divided into 5-folds of equal size. The best SNPs and their effects were estimated based on the lines in four of the folds and used for predictions of breeding values in the fifth fold. This was done to avoid unrealistically high predictive abilities that would be the result of using the same lines for estimation and prediction. The best SNPs were defined as the SNPs most significantly associated with the studied trait for the single marker regressions, and as the SNPs with the largest additive genetic effects for the Bayesian Power Lasso. When selecting SNPs using model 1, maximum one SNP was selected from each chromosome to avoid selecting several SNPs linked to the same QTL. Predictions were made using the SNP effects estimated in model 1. SNP effects were also re-estimated as random effects by fitting the selected SNPs simultaneously in either model 3 or in a SNP-BLUP model . Predictions were evaluated by calculating the correlation between observed phenotypes corrected for fixed effects and estimated breeding values.Grain from 635 winter wheat lines were phenotyped for the quality traits grain protein content, Zeleny sedimentation value, test weight, falling number, and TKW. The lines were from two different breeding cycles (set2014 and set2015). Phenotypic variation was observed for all traits, especially for Zeleny sedimentation and falling number, which had a coefficient of variation of 26.9 and 23.4%, respectively  and variance components based on the GBLUP and Bayesian Power Lasso models are shown in Table 10 showed that the observed p-values were inflated, i.e., most of the p-values were lower than the p-values expected for SNPs that were not associated with the studied trait. The genomic inflation factor (λIF)  are shown in Figure p-value = 2.5*10−6), 1D , and 5D   Figure . Based op-value = 4.3*10−5) with an allele frequency of 89% for the advantageous allele  with an advantageous allele frequency of 77% (results not shown).For falling number, a nearly significant region was found on chromosome 7B  and explained 1.7% of the genetic variance . Sorting the lines based on their genotypes for the associated SNPs for Zeleny sedimentation on chromosome 5D, 1D, and 1B, and looking at the mean of the phenotypic data, showed that these SNPs had a clear effect on Zeleny sedimentation  to continue to FThe three and ten best SNPs were identified for each trait using the single marker regression models and the Bayesian Power Lasso models. The correlation between observed phenotypes corrected for fixed effects and GEBVs based on these SNPs were calculated to compare the models.The correlations based on the best SNPs according to the single marker regression were higher than the correlations based on the Bayesian Power Lasso for grain protein content, test weight, falling number, and TKW Table . For ZelElite breeding material was used in the present study, so the number of significant SNPs (and their effects) were low compared with other studies, where the plant material had high diversity and larger phenotypic differences between lines , so the grain protein content was quite low. No SNPs were significantly associated with grain protein content, suggesting that this trait is controlled by many QTL with small effects. Furthermore, the relatively low heritability indicate that protein content is strongly affected by environmental effects and GxE interactions Shewry, . The wheThe SNPs most significantly associated with grain protein content were located on chromosome 2A, 4D, and 7A. In agreement with the present study, Groos et al.  identifiPina-D1 or Pinb-D1, which control grain hardness, are located on 5D and have been shown to be associated with several wheat quality traits including Zeleny sedimentation  .Regions associated with Zeleny sedimentation were also found on chromosomes 1B and 1D. Known loci that can affect gluten quality on these two chromosomes are the glutenin loci b-allele of the dwarfing gene Rht-D1 on chromosome 4D increased falling number. In addition, they found a QTL on chromosome 7B, which harbors the α-amylase gene α-Amy-B2 and a QTL associated with late maturity α-amylase content  based on phenotyped lines of previous sets. Only six lines  were used as crossing parents for both sets used in the present study. Nevertheless, the principal component analysis and G-matrix showed that the lines of the two sets were genetically related. The average genetic distance between the sets (0.76) was only slightly higher than within sets (0.74). This indicates that the crossing parents used for each set were genetically related. The genetic distance calculated as modified Rogers' distance can range from 0 to 1 (Reif et al., The LSO cross-validations resemble how the predictions would perform most realistically, when predicting lines of a new set before phenotypic information is available for those lines. However, the correlations based on the LSO were not as high as for the other types of cross-validations, because of a combination of a smaller training set size, lower genetic relationship between lines of the training and validation sets, and GxE interactions. The k-fold cross-validations showed that lowering the number of lines in the training set had a small negative impact on the correlations. Thus, the main reasons for the lower correlations of the LSO compared with the LOO and LFO were the decrease in genetic relationship between lines and GxE interactions. However, the effect of the genetic relationship may partly be confounded with the GxE interactions. Including data from more years, would most probably improve the results, which is the case in a recent study with spring wheat, where the predictive abilities for several quality traits increased as lines from more years were included in the training set (Battenfield et al., Bayesian models often perform better than GBLUP models when the genetic relationship between training and validation sets are low, because they are better at capturing LD between markers and QTL (Gao et al., Here, the largest improvement was for the LSO cross-validations for Zeleny sedimentation, when using the Bayesian Power Lasso model instead of the GBLUP model. Thus, the Bayesian Power Lasso model is mainly advantageous to use, if the genetic relationships between lines are low and for traits, where some QTL have large effects.SNPs significantly associated with Zeleny sedimentation were identified on chromosome 1B, 1D, and 5D, where genes that are known to affect baking quality of wheat are located. These three SNPs together explain 18.9% of the additive genetic variance according to the single marker regression analysis. The same genetic regions were identified using the Bayesian Power Lasso. However, the explained variance estimated in this model was considerably lower. The prediction of phenotypes based on the best three or best ten SNPs found using the two different methods revealed that the SNPs found using the single marker regression could more accurately predict the phenotypes in most cases. Predictions improved for all traits when using ten SNPs instead of three. The GWAS and predictions using few SNPs indicated that there was a couple of QTL with large effect on Zeleny sedimentation, while the other quality traits seemed to be controlled by many QTL with small effects. Genomic predictions based on all SNPs further improved the predictions and worked quite well for most traits. The predictive abilities were highest for Zeleny sedimentation, while grain protein content was the most difficult trait to predict, especially across breeding cycles. The different types of cross-validations indicated that the genetic relationship between lines and GxE interactions were more important for the predictive abilities and for the bias than the size of the training set. However, the predictions are based on single replication of lines, so additional replications across years and locations would be useful to study the effects of the GxE interactions.Using Bayesian Power Lasso models resulted in similar or slightly higher predictive abilities than when using GBLUP models.PK: performed most of the phenotyping, data analysis and wrote the draft for the manuscript; All authors helped designing the study, interpreting results, and reviewing the manuscript. Data was acquired by JA, JO, and PK. Funding was acquired by AJ, JA, JJ, and PK.The study was performed in a collaboration between Aarhus University and the plant breeding company Nordic Seed A/S. Authors PK, AJ, JA, and JO were employed by company Nordic Seed A/S. The other authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.