Caenorhabditis elegans, we made a discovery that the proportions of variant types are not constant across the C. elegans genome. The variant proportion is defined as the fraction of a specific variant type (e.g. single nucleotide polymorphism (SNP) or indel) within a broader set of variants . The proportions of most variant types show a correlation with the recombination rate. These correlations can be explained as a result of a concerted action of two mutation mechanisms, which we named Morgan and Sanger mechanisms. The two proposed mechanisms act according to the distinct components of the recombination rate, specifically the genetic and physical distance. Regression analysis was used to explore the characteristics and contributions of the two mutation mechanisms. According to our model, ~20–40% of all mutations in C. elegans wild populations are derived from programmed meiotic double strand breaks, which precede chromosomal crossovers and thus may be the point of origin for the Morgan mechanism. A substantial part of the known correlation between the recombination rate and variant distribution appears to be caused by the mutations generated by the Morgan mechanism. Mathematically integrating the mutation model with background selection model gives a more complete depiction of how the variant landscape is shaped in C. elegans. Similar analysis should be possible in other species by examining the correlation between the recombination rate and variant landscape within the context of our mutation model.Genetic diversity is maintained by continuing generation and removal of variants. While examining over 800,000 DNA variants in wild isolates of  Caenorhabditis elegans, we discovered apparent correlations between the recombination rate and the proportion of many variant types. To explain this correlation, we present a model of a concerted action of two groups of mutation mechanisms, which act according to different components of the recombination rate. This model can also explain how mutation mechanisms as a whole can affect the genomic landscape of the variant distribution. Using this mutation model, we systemically and holistically estimate the probabilities of generating specific mutation types by distinct groups of mutation mechanisms in C. elegans. Since this mutation model can be mathematically combined with existing natural selection models, such as background selection, a more comprehensive analysis of genetic diversity is now possible. We expect that the mathematical equations we present here can be used for refining computer simulations of evolution and coalescent modeling. Within the context of this mutation model, the correlation between the recombination rate and the proportion of variant types may serve as a useful new metric for analysis of genetic diversity in other species.DNA variants in the world population of a species reflect the genetic diversity of the species. While examining variants in whole-genome sequenced wild isolates of the nematode worm  Genetic diversity is maintained by interplay between the continuing generation and removal of variants; variants are produced by mutation and removed by genetic drift or natural selection during evolution. The modes of generating mutation are biologically diverse, and variants accumulate throughout the life history of a species . NaturalCaenorhabditis elegans, higher frequency of variants is observed in the regions of high recombination [Drosophila melanogaster early on [C. elegans, background selection in combination with selective sweep were shown to shape the variant distribution [C. elegans mutation accumulation (MA) strains does not show a correlation between the recombination rate and the accumulation of mutations and thus strongly argues against a substantial role of mutation [C. elegans [In many species including bination –7. Naturbination , but othbination , 10. Theearly on  but was early on , 12. In ribution , 14, butribution . The anamutation , 17, but elegans  and perh elegans –20.C. elegans, which had been whole-genome sequenced concurrently [C. elegans. In addition to explaining the correlation between the recombination rate and variant composition, our analysis suggests a greater importance of mutation in shaping the variant distribution in C. elegans than previously thought.In the present study, we performed a more complete examination of genetic diversity by a previously untried analysis of the composition of variants (e.g. the proportion of specific variant types), which complements the standard analysis of the distribution of variants (i.e. variant frequency and density). Here, we use the term proportion for a single specific variant type and the term composition for proportions of all variant types. Over 800,000 homozygous variants present in 40 wild isolates of urrently , form thWe discovered a striking pattern while examining the composition of variants such as indels of size between 40 and 699 base pairs (i40-699). The proportion of i40-699 out of all variants is higher near autosomal ends and lower in autosomal centers . For eve2 value. Correlation tests show a strong positive correlation between the recombination rate and the proportion of i40-699 out of all variants . A positive correlation means that the proportions of i40-699 out of all variants are higher in the regions of high recombination. A strong correlation raises the possibility of recombination rate being a causative factor in establishing different proportions of i40-699 out of all variants across the genome.The strength of correlation can be examined by a number of correlation tests including the methods of Pearson , SpearmaFor a more thorough analysis of variant composition, we examined the proportions of 30 variant types out of all variants, the proportions of 26 non-SNP subtypes out of all non-SNPs, and the proportion of transitions (Ts) and transversions (Tv) out of all SNPs. Indel variant types range from indels of single base pair change (i1) to indels of 100 to 4999 base pair change (i100-4999). We define non-SNP as variant types encompassing indels and substitutions of two or more adjacent base pairs as well as combination of these mutation types, which include variants without any change in the number of base pairs (i0) but is not a SNP. The proportions of SNPs out of all variants and transitions (Ts) out of SNPs showed strong negative correlation with the recombination rate with lower proportion in the regions of high recombination . A negat2 of 0.28 , and linear regression analysis shows a t of slope of 6.3 and R of 0.28 . The cor of 0.28 . Using S of 0.28 . TogetheThe correlation between the recombination rate and variant composition is similar among autosomes, but the correlation is often weaker for the X chromosome . InteresC. elegans [C. elegans have been placed into five groups [p values are shown in To further test the relevance of the correlation between the recombination rate and variant composition, we also examined the correlation between variant composition and several other genomic features. Other genomic features examined are exon density, coding DNA sequence (CDS) density, essential gene density using either the gene length or exon length, repetitive sequence density using inverted and tandem repeats, GC content, expression level, and five different measures of chromatin state. Some of these factors, including exon density and repeat sequence density, are correlated with the recombination rate in  elegans , 27. Chre groups , and some groups . DetailsUsing 58 definitions of the proportion of variant types, the correlations with the recombination rate show Pearson's r median absolute value of 0.5 . ExaminiThe distribution of variants was also examined as a comparison. Using the distribution of 31 different types of variants, the correlations with the recombination rate show a Pearson's r median value of 0.70 . ExaminiWe asked whether exon density or repetitive element density, which are correlated with the recombination rate, might be responsible for the existing landscape of variant composition rather than the recombination rate. First, we examined the correlation using only the variants that affect exons as opposed to using the variants that do not affect exons. By Pearson's r, similarly strong correlations are observed using all variants  and using only the variants that do not affect exons  . On the As for repetitive sequence density, we examined the correlation using only the variants that affect DNA outside repetitive sequences. This was done because examining the correlation by separating variants into those that affect and those that do not affect repetitive sequences was less satisfactory  Tables. Here, we discuss forces that can affect variant composition, and we will consider natural selection first. Natural selection, which acts by the fitness of phenotype, can be divided into the direct natural selection of non-neutral variants and the collateral removal of neutral variants, which depends on the linkage or the recombination rate between the selected non-neutral variant and nearby neutral variants. In the latter case, linkage-based selection models, such as selective sweep  and backp < 0.001) in the proportions between these variant populations. The difference is even greater if the variants that affect CDS are examined instead . In comparison, the variant composition is similar for the variants that affect introns but not exons and for the variants that affect neither coding sequences nor introns  compared to an interval of 1 Mb. A key underlying assumption is that the probability of mutation being generated is equal from one nucleotide to the next nucleotide. For example as a chromosome is replicated by a DNA polymerase, one nucleotide is as likely to become a site of mutation as the next nucleotide. The probability of mutation being generated at each base pair position during replication is assumed to be a constant. We named this group of mutation mechanisms as the Sanger mechanism for the critical role that the Sanger sequencing method played in determining the physical distance of DNA. We note that some chemical mutagens and irradiation may affect some nucleotide more than others, and homopolymers may be more liable to slippage resulting in a loss or a gain of base pairs. Such caveats aside, the number of variants generated by the Sanger mechanism for a genomic interval of a given physical length is defined as follows:Next, consider the mutation mechanisms that act according to the genetic distance. Such mechanisms would generate twice as many variants in an interval of 2 centimorgans (cM) compared to an interval of 1 cM. Using the strictest definition, the probability of mutation generation here depends on the probability of a base pair position becoming a site of meiotic chromosomal crossover. We call this group of mutation mechanisms as the Morgan mechanism. Unequal crossover of chromosomes leading to mutation has been known from the early days of modern biology , and dirC. elegans genome would involve 100,000,000,000 base pairs with a probability of mutation at each base pair, and the sum of the probabilities should be multiplied by the average number of cell cycles involved going from one generation to the next. The number of variants generated by Morgan and Sanger mechanism in a single generation is defined as follows:To formulate a mathematical model that combines the effect of the Morgan and Sanger mechanisms, the contribution of the two mechanisms needs to be normalized to the same time scale. Therefore, both Morgan and Sanger coefficients should reflect the number of potential mutation generation events in a single generation. For example, the probability of mutation generation by the Morgan mechanism should be modified by ten if there are ten programmed meiotic DNA double-strand breaks in the life cycle of an organism starting from a fertilized egg to the next fertilized egg. Replication of a 100 Mb There is a fixed ratio that describes the relative relationship between the Morgan and Sanger coefficients. We call this the R coefficient:Relative contributions of the Morgan and Sanger mechanisms can be written as shown below using the R coefficient and without the S coefficient:See M defines the probability of generating a specific variant type by a Morgan mechanism mutation generation. Likewise, FS defines the probability of generating a specific variant type from a Sanger mechanism mutation generation. An FM of 1 or 0 for SNP means that the Morgan mechanism generates SNP with a probability of 100% or 0%, respectively. The proportion of a specific variant type in an interval is:To explain the correlation between the recombination rate and variant composition, we need to discuss the probability of generating a specific variant type. The key assumption here is that there is a fixed probability of a mutation generated being a specific mutation type for each mutation mechanism. Thus, we expect that Morgan and Sanger mechanisms would have different probabilities of generating a specific mutation type. The coefficient FM + R * FS) may correspond to the number of a specific variant type, and the denominator (r + R) may correspond to the number of all variants in the interval. The same equation can be used with denominator being something other than all variants  regression analysis [Using the equation for the proportion of specific variant type, it should be possible to estimate the Fanalysis , 39. A sanalysis , and theC. elegans chromosomes  and a pair of the isolates (ED3057 and ED3072) are nearly identical throughout the entire genome, as also noticed by others ; ED3072,M and FS are 0.67±0.02 (standard error of the estimate) and 0.72±0.00, respectively  and 9.2 with p < 0.01 (n = 17) . Given these estimates and their accompanying supporting statistic values, it seems reasonable to propose an approximate R coefficient value of 10 for C. elegans. The estimates of FM and FS coefficients presuming a uniform R coefficient value (e.g. R = 10) are presented in C. elegans are generated by the Morgan mechanism in the wild environment.The quality of the R and F coefficient estimates can be assessed by examining the associated t and e of 9.6 . Thirty-(n = 17) . Using Bp < 0.05 cutoff, It is possible that the proposed R coefficient value of 10 is too big. With additional processing of overlapping variants and censoring of overshadowed variants see , the medM and FS coefficient estimates from LS regression analysis using a presumed the value of the R coefficient. By definition, the FM and FS coefficients must be in a range between 0 and 1. Thus, we declared that a presumed R coefficient value that suggests an FM or FS coefficient value outside this range is incorrect. We examined the estimates of the FM and FS coefficients using presumed R coefficient values between 0.01 and 9900. Here, an upper limit of 57 for the R coefficient is suggested by the analysis of indels of 1 base change (i4) out of non-SNPs whereas a lower limit of ~0.9 is suggested by i40-699 out of all variants , which indicate a higher degree of confidence than the R coefficient estimates derived from the analysis of variant composition. Using all variants and the variants that do not affect CDS instead, R coefficient estimates are 3.3±1 and 3.5±0.9 . Again, our standard analysis uses the variants that do not affect exons. Here, the estimate of the R coefficient is 3.5±0.9 , and the 3.5±0.9 . The DNA 3.5±0.9 .The discrepancy in the R coefficient estimates between the analysis of variant distribution and the analysis of variant composition can be reconciled. Earlier, we mentioned that linkage-based selection models could also explain the skewing of distribution of variants according to the recombination rate. This means that a proper analysis of the correlation between the recombination rate and variant distribution must account for both mutation and the Hill-Robertson effect in general (e.g. through background selection or selective sweep). On the other hand, the Hill-Robertson effect can be ignored in the analysis of variant composition. This means that an R coefficient of 10 from the analysis of variant composition reflects the action of mutation only whereas an R coefficient estimate of 3.5 from the analysis of variant distribution reflects the combined action of mutation and selection.C. elegans. A combined model containing both the background selection and our mutation model can be made by a coupling of the equations from the two models as follows:A more complete depiction of how the variant landscape is shaped is possible by combining our mutation model with a linkage-based selection model that also affects variant distribution according to the recombination rate. We chose background selection for a demonstration here because background selection is generally assumed to have a greater effect than selective sweep in o = (r + R) * d * n * M was used to substitute the number of variants without background selection (vo) in the background selection equation. Here, vb is the number of variants after background selection, U is the deleterious mutation rate, sd is the average selection coefficient, and F is the inbreeding coefficient, with a relationship to the outcrossing rate, c: F = (1-c)/(1+c) [d and F coefficients should have values between 0 and 1. Because background selection does not affect variant composition, the R coefficient estimate from the analysis of variant composition should be used here.Here, mutation model equation vc)/(1+c) , 7. BothC. elegans has been measured by many approaches with a wide range from 0.003 to 0.48, and 0.48 seems to be the current accepted value [C. elegans has been estimated in a range between ~1% and 1.7% previously [Others have determined some of the values used in the background selection model. The deleterious mutation rate (U) in ed value –49. The eviously –52, exceeviously . Thus, wd selection coefficient vary depending on the assumed values of the R coefficient and M * d . In comparison, R2 is 0.48 using the mutation model alone with the R coefficient of 3.5. Our opinion is that the differences in the R2 values are too small to be used to pick the value of the R coefficient. Nevertheless, these analyses using the combined model allow a fuller exploration of how variant landscape have been generated than by using a single model.The estimates of the snd M * d . Here, ovariants . We suspM for SNP of 0.8, and FS for SNP of 0.7 without selection, introducing the action of selection that removes 50% of the indels and none of the SNPs would change the variant composition so that LS regression analysis would generate an apparent R coefficient estimate of 10.6 instead of 10. Selection is likely to remove indels more than SNPs and larger indels more than smaller indels, and FM values are larger than FS values for most indel types for C. elegans. Thus, selection in most cases would reduce rather than amplify the difference in the variant composition between the regions of low and high recombination. This means that our R coefficient estimates probably underestimate the real contribution of the Morgan mutation mechanism. We suspect that selection would discriminate between indels and SNPs to a lesser degree than in the example given here (i.e. 50% versus 0%), and thus the actual effect on the estimation of the R coefficient is probably smaller. As discussed earlier, DNA repair and apoptosis in direct response to mutation can also affect variant composition in a similar manner.If mutation can generate a disparity in the landscape of variant composition according to the recombination rate, then natural selection theoretically can amplify or reduce the disparity by a simple mechanism. Take a scenario where two genomic regions accumulate different numbers of variants in the absence of selection (e.g. region A with 500 indels and 500 SNPs and region B with 20 indels and 80 SNPs). For simplicity, all variants are outside exons. Now, extend the scenario so that selection removes a higher percentage (e.g. 50%) of the indels and a lower percentage (e.g. 0%) of the SNPs. Here, selection has changed the variant composition (and distribution) to a different degree for the two regions, and the recombination rate is one of the underlying factors. In a simulation using the pf boundary definition, the real R coefficient value of 10, Fp < 0.05 using pf, pr, gf, and gr interval boundary definitions, respectively). After aggregating the data using all four boundary definitions, the median R coefficient estimate is 7.2, which suggests a 32% contribution by the Morgan mechanism. It should be noted that the associated t and p values obtained using aggregated boundary definitions should be treated differently than when single boundary definition is used. Notably in the analysis of variant distribution, the R coefficient estimate also drops to 2.5 with the aggregated data using all four boundaries  using the standard pf boundary definition and 35±18 (p = 0.05) using all four boundary definitions together. These R coefficient values suggest a 4% or 9% contribution by the Morgan mechanism, respectively. Meaningful analysis is not possible with variant composition in MA strains because the total number of MA variants is very small (n = 391). The authors of the MA strains suggested that the unequal distribution of variants in the wild population is likely a result of natural selection and not mutation. However, the generation of mutations in MA strains perhaps does not accurately reflect the generation of mutations in the wild environment, which is a possibility also suggested by the authors of the MA strain studies [C. elegans. If this is true, mutation-accumulating strains grown in laboratory may be irrelevant for studying the relative importance of Morgan and Sanger mutation mechanisms in the wild environment.A potential argument against our proposed R coefficient values between 4.8 and 10 comes from the analysis of mutation-accumulating (MA) strains , 17, whi studies , 17. PerC. elegans genome. We used this mutation model to systemically and holistically estimate the probabilities of generating specific mutation types by the putative Morgan and Sanger mechanisms in C. elegans. Since this mutation model is compatible with existing natural selection models, such as background selection, a more comprehensive analysis of genetic diversity is now possible. We think that this new metric of the proportion of variant types together with our mutation model have a potential to be generally useful in the analysis of genetic diversity in other species. It would be especially interesting to see if a substantial contribution of Morgan mechanisms in mutation generation is the rule rather than an exception when variant composition is examined in other species including in humans.In this study, we showed that examining the composition of variants has a potential to reveal many interesting facets of molecular evolution. The proportions of many variant types in different genomic intervals show strong correlation with the recombination rate. By separating mutation mechanisms conceptually according to those dependent on genetic and physical distances, our mutation model describes how the composition of variant as well as the distribution of variants in the genome may become uneven throughout the For computational processing and analysis, custom scripts were written and executed using R  and R StC. elegans variant data and genomic features were obtained using the newest version WS256 of WormBase (http://www.wormbase.org) [http://www.wormbase.org/tools/genome/gbrowse/c_elegans_PRJNA13758/). Specifically, the variants were obtained by using Polymorphisms track of GBrowse. Other GBrowse tracks used were: Curated Genes, Curated Genes (Protein-coding), Curated Genes (noncoding), RNAseq for expression level, Tandem and Inverted Repeats for repetitive sequences, and various Histone Modifications ChIP-Seq  for chromatin state. GFF3 files were obtained using GBrowse in all cases except WIG  files were obtained for chromatin state. Curated Genes contain the details on genetic and physical location as well as exons and introns, and Curated Genes (protein-coding) and Curated Genes (noncoding) contain the information specific to coding DNA sequences and non-coding RNA, respectively. ChIP-seq and RNAseq data were generated by the modENCODE project [C. elegans genomic DNA sequence [ftp://ftp.wormbase.org/pub/wormbase/species/c_elegans/sequence/genomic/). To obtain a list of essential genes, we used the queries lethal, sterile, larval lethal, larval arrest, embryonic lethal, and zygotic lethal as mutant phenotypes using WormMine version WS253 (http://intermine.wormbase.org/tools/wormmine/begin.do).The ase.org) . Most ofWe use four sets of interval boundary definitions . Two setThe total exon space was calculated after accounting for duplicates and overlaps. Specifically, duplicate exons that share the same 5' and 3' ends were removed. Overlapping exons were combined into one exon. Any exon that is located completely within another exon was removed. The same process was used to calculate the genomic space occupied by essential genes, the genomic space occupied by the exons of essential genes, and the genomic space occupied by repetitive sequences. For introns, an additional process of subtracting the space occupied by exons within introns was performed. The density of these elements is defined as the physical length of space occupied by the element (e.g. exons) divided by the physical length of the genomic interval.RNAseq GFF3 file was used to calculate expression level, and WIG files were used to measure chromatin state. Briefly, we multiplied the interpreted depth of coverage by RNAseq by the length of each RNAseq reads. To obtain normalized expression level for each genomic interval, we then divided the sum of these products by the total length of the genomic interval. Similarly, the sum of the levels of methylation state for 10 base pair stretches in WIG files were obtained for each genomic interval. To obtain normalized chromatin state level for each genomic interval, we divided this sum by the number of the 10-base pair stretches corresponding to each genomic interval.The variant data obtained from WormBase using the Polymorphisms track of GBrowse contain a great deal of information. The information includes the start and end positions of the variants relative to the N2 reference genome. Other information includes a list of wild isolates with the variant and the consequence of the variant on the protein coding sequence.C. elegans wild isolates with variant data. The reason for choosing these 40 isolates was that these 40 have been sequenced via whole-genome sequencing by the Million Mutation Project (MMP) and thus have the most complete data. The 869,019 variants in the 40 wild isolates account for over 97% of all natural variant records in the WS256 WormBase polymorphism data. Four different methods were used by the MMP to identify variants [http://genome.sfu.ca/mmp/), but the physical position of the variants in the MMP curation often does not perfectly match the reference genome position provided by WormBase. Many of the variants annotated by WormBase were identified over a long period of time for some of the 40 wild isolates. Other methods of variant identification included light shotgun sequencing [We focused solely on 40 wild isolates out of hundreds of variants , specifiquencing , 57 and quencing , 58, 59.We found many inconsistencies of annotation in the WormBase curated variants, including adjacent, overlapping, and overshadowed variants. For example, substitutions of two or more adjacent base pairs are often not curated as a single variant even in cases of the adjacent variants being present in an identical set of wild isolates. Combining such adjacent variants seems absolutely warranted. More complicated are a small number of variants occupying an overlapping space in the genome. Arguably the most consequential are a large number of variants that are completely enveloped, or overshadowed, by a large deletion. Overlapping and overshadowing of variants may stem from complex genome rearrangement, such as a combination of deletion(s) and duplication(s). Another possible source of inconsistency is the differences in sample sources, but we found many similar inconsistencies using only the MMP data. Therefore, the main problem appears to be different results derived from multiple independent variant calling methods and a lack of a thorough and holistic reconciliation of the conflicting results.After combining all adjacent variants that are present in identical set of wild isolates, the total number of variants was reduced from 869,019 to 853,815. Our main analysis was performed using these 853,815 processed variants either as a whole or as an aggregation in 37 of the 40 wild isolates. For further processing involving overlapping and overshadowed variants, we did not require that the variants of interest are present in identical set of wild isolates. Overlapping and overshadowing variants were processed at the level of individual wild isolates only, and these more processed variants were used for supplementary analysis. Overlapping variants were combined into a single variant, and overshadowed variants were censored. In part because of the presence of some very large indels including 144 variants of >100,000 base pair deletions (including a deletion of >1.4 Mb), this process reduced the number of variants by 11% to 28% depending on the wild isolate (median = 19%).The location of the variants was annotated relative to exons, introns, CDS, ncRNA, and repetitive sequences. The results of this annotation at the whole-genome level are summarized in WormBase annotations were used to check our annotation results that were examined relative to CDS . All but 70 variants that we annotated as affecting CDS had WormBase annotation term = Nonsense, = Frameshift, = Silent, = Coding_exon, or = Readthrough. In the case of these 70 exceptions, WormBase used the annotation term = Splice_site instead. The conflict is there because WormBase used a shorter exon rather than a larger exon in these 70 cases. Conversely, our annotation of the variants that affect CDS missed 26 variants that WormBase annotated with the terms = Frameshift or = Coding_exon. Of these 26, WormBase correctly annotated 14 insertions affecting splice site as = Frameshift. WormBase annotation looked incorrect to us in the other 12 cases.S1 Text(DOCX)Click here for additional data file.S1 TableRelationship between the recombination rate and the proportion of variant types were examined by correlation tests and linear regression analysis. Total of 58 definitions of the variant type proportion were examined.(CSV)Click here for additional data file.S2 TableRelationship between the recombination rate and the distributions of variants were examined by correlation tests and linear regression analysis. Total of 31 variant types were examined.(CSV)Click here for additional data file.S3 TableRelationship between the proportion of variant types and other genomic features were examined by correlation tests and linear regression analysis. Other genomic features are exon density, CDS density, essential gene density, essential gene exon density, repetitive sequence density, GC content, RNAseq level, and chromatin state.(CSV)Click here for additional data file.S4 TableRelationship between the distribution of variants and other genomic features were examined by correlation tests and linear regression analysis.(CSV)Click here for additional data file.S5 TableRelationship between the recombination rate and the proportion of variant types were examined by correlation tests and linear regression analysis using the variants that do not affect exons.(CSV)Click here for additional data file.S6 TableRelationship between the recombination rate and the proportion of variant types were examined by correlation tests and linear regression analysis using the variants that affect exons.(CSV)Click here for additional data file.S7 TableRelationship between the recombination rate and the proportion of variant types were examined by correlation tests and linear regression analysis using the variants that affect repetitive sequences.(CSV)Click here for additional data file.S8 TableRelationship between the recombination rate and the proportion of variant types were examined by correlation tests and linear regression analysis using the variants that do not affect repetitive sequences.(CSV)Click here for additional data file.S9 TableRelationship between the recombination rate and the proportion of variant types were examined by correlation tests and linear regression analysis using the variants that affect the DNA outside repetitive sequences.(CSV)Click here for additional data file.S10 TableRelationship between the recombination rate and the proportion of variant types were examined by correlation tests and linear regression analysis using the variants that only affect the DNA inside repetitive sequences.(CSV)Click here for additional data file.S11 TableBreakdown of the total number of variant types are given for all variants as well as for the variants that affect or do not affect exons, CDS, repetitive sequences and other features.(CSV)Click here for additional data file.S12 TableThe four boundary definitions  and their characteristics are described.(CSV)Click here for additional data file.S13 TableThe results of analysis are shown using the aggregated data from 37 wild isolates.(CSV)Click here for additional data file.S14 TableThe results of analysis are shown using the aggregated data from 37 wild isolates.(CSV)Click here for additional data file.S15 TableThe results of analysis are shown using the aggregated data from 37 wild isolates.(CSV)Click here for additional data file.S16 TableOverlapping variants were combined, and overshadowed variants were censored. The variants that affect exons were censored. The results of analysis are shown using the aggregated data from 37 wild isolates.(CSV)Click here for additional data file.S17 TableThe results of analysis are shown using the variants that do not affect exons without data aggregation.(CSV)Click here for additional data file.S18 TablePresumed R coefficient values are 6, 10 and 60.(CSV)Click here for additional data file.S19 TableThe results of analysis are shown using all variants, the variants that do not affect exons, and the variants that do not affect CDS.(CSV)Click here for additional data file.S1 FigChromosomal patterns are shown for the proportion of i40-699 out of all variants (A), proportion of SNPs out of all variants (B), recombination rate (C), exon density (D), intron density (E), repetitive sequence density (F), GC content (G), and expression level (H).(TIF)Click here for additional data file.S2 FigCorrelations are shown for the proportion of i40-699 out of all variants (A), the proportion of SNPs out of all variants (B), the proportion of i40-699 out of non-SNPs (C), the proportion of transitions (Ts) out of SNPs (D), and the distribution of all variants (E).(TIF)Click here for additional data file.S3 FigAnalysis using the variants that affect exons, the variants that do not affect exons, the variants that affect introns but not exons, the variants that affect neither CDS nor introns, the variants that affect repetitive sequences, the variants that do not affect repetitive sequences, the variants that are located inside repetitive sequences, and the variants that are not inside repetitive sequences. Correlations are shown for the proportion of i40-699 out of all variants (A), the proportion of SNPs out of all variants (B), the proportion of i40-699 out of non-SNPs (C), and the proportion of transitions (Ts) out of SNPs (D).(TIF)Click here for additional data file.S4 FigM (black) and FS (red) obtained with presumed R coefficient value in the x-axis while examining the correlation between various variant type proportions and the recombination rate. Vertical hatched lines indicate the lower and upper limits of acceptable R coefficient values. The lower limit of the acceptable R coefficient was not determined for i1/variants, i4/variants, and i4/non-SNPs.Estimates of F(TIF)Click here for additional data file.


Hd3a, qGL3, OsmiR156h, and LAX2, were identified as candidates within these QTLs. Nearly forty percent of the QTLs had only two genotypes in the F1 hybrids, mainly because the maternal lines were under intense selective pressure. Further analysis found male sterile lines and restorer lines made different superior allele contributions to F1 hybrids, and their contributions varied among different traits. These results extend our understanding of the molecular basis of heterosis in two-line hybrid rice.Heterosis has been widely utilized in agriculture and is important for world food safety. Many genetic models have been proposed as mechanisms underlying heterosis during the past century, yet more evidence is needed to support such models. To investigate heterosis in two-line hybrid rice, we generated a partial diallel crossing scheme, which consisted of approximately 500 F1 hybrids derived from 14 male sterile lines and 39 restorer lines. In this population, increased panicle number played the most important role in yield heterosis of hybrid rice. Genome-wide association studies identified many QTLs related to the yield traits of F1 hybrids, better paternal heterosis and special combining ability. Relevant genes, including  In China, rice production occupies 18.3% of total farmland (corn occupies 24.4%); hybrid rice was sown in approximately 12.8 million ha in 2014, whereas conventional rice was sown in approximately 11.1 million ha (Crop Seed Industry Development Report in China (2015)). In 1973, a three-line hybrid rice system composed of one cytoplasmic male sterile line, one maintainer line, and one restorer line was successfully developed in China2. Then in the 1980s, a two-line hybrid system, composed of one environment-sensitive genic male sterile (EGMS) line and one restorer line, was developed3. The two-line system has several advantages over the three-line system, including easy male sterile line multiplication , no restriction with regard to the restorer line , and easy use of inter-subspecific heterosis 4. While commercial hybrid rice is estimated to outperform conventional inbred rice by >20% in grain yield, two-line commercial hybrid rice is estimated to outperform its three-line counterpart by ~10% in grain yield4. Therefore, the two-line hybrid rice system has become increasingly important in hybrid rice breeding5.Asia produces more than 90% of rice, which supplies one quarter of the total calories consumed by the world population and is the main food for most of the world’s poor8. Since George H. Shull rediscovered heterosis in 19089, many hypothetical genetic mechanisms, including dominance11, overdominance13, epistasis16, gene balance18, and protein quality control20 have been proposed to explain heterosis. Today, most heterosis studies mainly focus on important agronomic traits in crops such as corn and rice. Due to the quantitative nature of these traits, many genetic mechanisms likely function in heterosis; therefore, it is probable that no single genetic mechanism can adequately explain all aspects of the heterosis phenomenon21.Although heterosis, or hybrid vigor, has been successfully used in hybrid rice production, as well as in production of many other crop species, including corn and sorghum, its genetic mechanism remains unclear28. The accuracy of early genetic mapping suffered from the use of low-density markers; for example, the mapping resolution was low and did not allow differentiation between overdominance and pseudo-overdominance. Most of these studies used parental materials derived from bi-parental mapping populations, and the genetic diversity among these parental materials was very low. Therefore, the genetic mechanisms derived from studies of these populations might be of little relevance to actual hybrid rice production, as many genetically diversified male sterile lines and restorer lines are currently used in hybrid rice breeding. With the rapid development of genome sequencing, genome-wide association study (GWAS) using high-density genetic markers has been widely used to dissect the genetic mechanisms underlying quantitative traits in crop species29. In rice, GWAS has proven to be a useful tool for identifying important genes related to agronomic traits31. Recently, Huang et al. genotyped 10,074 F2 lines derived from 17 representative varieties from 3 different hybrid rice systems, revealing many important genes related to 7 yield-related traits33. These studies indicate that genetic mapping in a multi-parental population using high-density markers could be utilized to discover the genetic basis of heterosis.In the past twenty years, genetic mapping of the loci underlying rice heterosis using molecular markers has been performed34. In hybrid rice, better paternal heterosis  is most important to breeders because the female parent is sterile. Special combining ability (SCA), a very important indicator when selecting for superior hybrid cultivars in rice breeding, is mainly affected by non-additive effects such as dominance and epistasis35. Identification of the genetic mechanisms underlying better paternal heterosis and SCA is of practical importance in hybrid rice production.Although middle-parent heterosis (superior performance of the F1 hybrid in comparison with the average of both parents) was of great interest in previous heterosis analysis, better-parent heterosis (superior performance of the F1 hybrid in comparison with the better parent) is the major goal underlying the wide adoption of hybrid techniques in agriculture because of its economic impactIn hybrid rice breeding, male sterile lines and restorer lines are under quite different selective pressures. In addition to sterility, male sterile lines have to be dwarfed (facilitating pollination), show early-heading (short growing period), and have good combining abilities for many agronomic traits. Therefore, the breeding of male sterile lines requires much more effort than that of restorer lines. In addition, male sterile lines have a demographic history quite different from that of restorer lines, as the former are all derived from several main ancestors, while the latter have a much broader genetic origin. Therefore, the genetic architectures underlying many traits in male sterile lines are probably quite different from those that underlie the same traits in restorer lines, and these differences may have distinct impacts on the agronomic performance of F1 hybrids.In this study, we constructed a partial diallel two-line hybrid rice cross scheme and measured heterosis in nine yield-related traits. We performed GWAS and identified genetic loci underlying better paternal heterosis and SCA in the hybrid rice lines. We found that the superior allele ratios of many QTLs differed markedly between the male sterile lines and restorer lines. Furthermore, we screened for genetic regions under selective pressure in both male sterile lines and restorer lines, revealing the role of selective pressure in the heterosis phenomenon in F1 hybrids. All the genotype and phenotype data used in this study is provided in Supplementary Data In this experiment, fourteen photo-thermo-sensitive genic male sterile  lines that have been widely used in commercial hybrid rice breeding in China were used as maternal lines, and three core recombinant inbred lines (RILs) (each consisting of 12–14 lines) were used as restorer  lines. Each restorer line was crossed to all 14 male sterile lines, yielding a partial diallel cross panel consisting of 500 F1 hybrids. Field experiments were first performed in Changsha (CS), China, in the summer of 2014, after which they were performed in Lingshui (LS), China, in the spring of 2015. Nine agronomic traits (heading date (HD), plant height (PH), panicle number per plant (PN), seed number per panicle (SNPP), grain yield per plant (GYPP), 1000 grain weight (TGW), grain length (GL), grain width (GW), and grain length/width ratio (GLWR)) were evaluated. All nine traits showed a continuous distribution , suggesting the same association signal in the F1 GWAS and BPaV GWAS. F1 GWAS (CS) using other inheritance models detected three more QTLs located on chromosomes 3, 4, and 11. A QTL located on chromosome 3 and harboring OsETOL1, which encodes a protein that controls ethylene biosynthesis and spikelet fertility47, was also discovered via the BPaV, SCA, and MPV GWAS of HD for the LS dataset  was identified by the F1 GWAS in the CS dataset when the additive inheritance model was used. This QTL explained 41.8% of the HD variance in the CS dataset. Another QTL (lead SNP: R0921365484AG), located approximately 65 kb downstream of F0921300849AC, was found in the BPaV GWAS of HD for the CS dataset, and it explained 30.8% of the HD_BPaV (representing the BPaV of HD in the F1 hybrids) variance. These two lead SNPs were in strong linkage disequilibrium . Five genomic regions (shorter than 250 kb) located on chromosomes 3, 10, 11, and 12 were shared by the F1 GWAS and BPaV GWAS results. However, all of these regions had differently located association signals, and only one of them (on chromosome 10) showed high linkage (r2 = 0.87) between the two lead SNPs identified by the F1 GWAS and BPaV GWAS. The F1 GWAS and BPaV GWAS of SNPP for the LS dataset each identified 5 and 6 QTLs, among which 2 QTLs (lead SNPs: R0605948297AG and R0626712051CA) were shared by both sets of results  Fig. . The F1 lts Fig. . Lead SN52. For HD, the previous BPaV GWAS for the CS dataset identified 14 QTLs, of which 4 were shared by the F1 GWAS results. After using HD_F1 as a covariate, only 5 of the 14 QTLs remained in the new BPaV GWAS results, including 3 of the 4 overlapping QTLs, but not the QTL located on chromosome 4  in comparison with those removed from the BPaV GWAS results (32.4% for CS and 33.3% for LS). The QTLs that were removed from the new GWAS analysis occurred at low frequencies in the previous BPaV and SCA GWAS  suggest that the genetic architectures underlying BPaV and SCA might be quite different from those underlying the original F1 hybrid phenotypes, and the QTLs identified in the BPaV and SCA GWAS might not directly affect the original F1 hybrid phenotypes. We re-ran the BPaV and SCA GWAS with the original F1 hybrid phenotypes added as covariates. This pleiotropy analysis aimed to remove the impact of QTLs directly influencing the original F1 hybrid phenotypes and to identify QTLs independently affecting BPaV or SCAe 4 Fig. . This fie 4 Fig. . This fiOsmiR156h  in F1 hybrids. However, not all QTLs had all three genotypes in the F1 hybrids assessed in this study. For the F1 GWAS results, most of the QTLs (76.1% for CS and 85.2% for LS) had all three genotypes in the F1 hybrids, while the others had only two genotypes (Aa and either AA or aa). For the BPaV GWAS results, approximately half of the QTLs (44.1% for CS and 55.6% for LS) had all three genotypes. For the QTLs underlying SCA, 61.2% of CS QTLs and 52.7% of LS QTLs had all three genotypes. Therefore, we separated all QTLs into two groups, a three-genotype group and a two-genotype group, according to their genotype varieties in the F1 hybrids. For QTLs in the three-genotype group, a linear regression model was used to assess the relative contributions of dominance and additive effects for each QTL, revealing that most three-genotype QTLs (70.1% for CS and 82.5% for LS) showed non-additive effects, indicating the predominant roles of non-additive effects in heterosis Fig. . Many QT56h Fig. , showed 56h Fig. . The othTwo-genotype QTLs were further separated into two groups according to the relative performance of heterozygotes and homozygotes. When the average phenotype value of heterozygotes (Aa) outperformed that of homozygotes (AA or aa), the two-genotype QTL was placed into the hetero-superior group; otherwise, the QTL was placed into the homo-superior group. The hetero-superior and homo-superior groups had nearly equal numbers of two-genotype QTLs for the BPaV GWAS results (27/30 for CS and 22/22 for LS). However, for the SCA GWAS results, the hetero-superior group outnumbered the homo-superior group by 32/13 in the CS dataset and 40/30 in the LS dataset.In our crossing design, we can easily trace the parental origin of superior alleles for each QTL and measure the superior allele contributions from both parents. For large proportions of QTLs . In addition to SNPP_BPaV and GYPP_BPaV, we also found this QTL to be associated with TGW_BPaV . This result is in concordance with the fact that the male sterile lines are all dwarfs due to strong artificial selection. Genes controlling rice height, including LU1 Fig.  and OsPDDK1 Fig. , were id−5 (LS), two-sided Student’s t-test, Supplementary Fig. For three-genotype QTLs, non-additive QTLs with negative effects identified in the SCA GWAS had much lower superior allele ratios (29.0% for CS and 23.4% for LS) in the male sterile lines in comparison with those of positive non-additive QTLs (44.3% for CS and 56.4% for LS) (p = 0.037 (CS) and p = 2.52 × 10DIF, OsLG1, OsASR1, Ghd8, and OsCESA9, were found within these regions . These methodological shortcomings should be remedied in future studies of rice heterosis.In this study, GWAS identified many QTLs related to heterosis in hybrid rice. However, the marker density was very low (approximately 0.11 SNP/kb); therefore, many important variations, including rare SNPs, copy number variation, and indels, were not identifiable. Future studies using resequencing techniques will allow most genome variations to be captured, thus revealing their relationships with heterosis. Moreover, the relatively low number of parental lines used in this study resulted in low-resolution GWAS signals. The use of many genetically diversified parental lines can greatly improve GWAS resolution and allow pseudo-overdominance and overdominance to be distinguished. Although resampling GWAS using a mixed linear model can greatly reduce false positive signals, many real associated genetic loci can be eliminated due to their relationship with population structure  was derived from elite cultivars Chenghui-448 and Minghui-86. RIL G3509 (13 lines) was derived from elite cultivars Huahui-451 and 2837. RIL G4363 (14 lines) was derived from elite cultivars 2293–622 and 2464. All parental lines were used in commercial hybrid rice breeding and showed good combining ability. Each paternal line was crossed to all 14 female lines by hand pollination to derive a partial diallel cross scheme. F1 hybrids and their male parents were planted in Changsha, China, in the summer of 2014. F1 hybrids and both of their parents were planted in Lingshui, China, in the spring of 2015. All female parents were completely sterile in the high temperature summer environment of Changsha. In the low temperature spring environment of Lingshui, the female parents were partially sterile, so some panicles could be fertile depending on the temperature (threshold temperature: approximately 23.5 °C). All planting followed a randomized complete block design. Three replicates of each variety were evaluated in Changsha. Two replicates of each variety were evaluated in Linshui because of a shortage of F1 hybrid seeds. Each plot consisted of two rows with six plants per row. The distance between plants in each plot was 18.33 cm. The distance between plots was 36.66 cm. The field was managed according to normal agricultural practice. True F1 hybrids were determined by careful examination of morphological traits, including heading date, plant architecture, and grain shape. F1 hybrids with ambiguous identities were abandoned. Finally, 458 F1 hybrids from the CS dataset qualified for further phenotype evaluation, whereas 471 F1 hybrids from the LS dataset qualified for further phenotype evaluation.Heading date was recorded per plot as the time from sowing to the day that half of all plants in that plot had emerged panicle flowers. The other traits were evaluated after harvesting, and only the middle 8 plants in each plot were harvested for further measurements. Plant height was evaluated as the length from the soil surface to the end of the main panicle. A panicle was counted if it had more than 10 full-filled grains. All grains were dried (moisture between 13% and 14%) before further evaluation of traits related to gain yield and grain shape. Approximately 600 grains were used to measure grain shape-related traits . SNPP was measured using the following formula: All 53 parental lines were genotyped using the rice 50 K SNP chip on the Illumina Infinium platform. This SNP array contains 51478 SNPs that are evenly distributed on all 12 chromosomes. First, we filtered the genotypes of the parental lines by the following criteria: missing rate <= 0.2 (4466 SNPs removed) and heterozygous rate <= 0.15 (another 1596 SNPs removed). The filtering process left 45416 high quality SNPs, among which 26920 SNPs showed polymorphism and were used for further analysis. We used the KNNcatimpute function (R package ‘scrime’) to perform genotype imputation. To increase imputation accuracy, we added the high-quality genotypes of 337 closely related rice cultivars to form an imputation panel consisting of 390 samples. We evaluated the imputation accuracy by random sub-sampling validation, and the accuracy rate was ~98.5%. After imputation, we obtained F1 hybrid genotypes by combining their corresponding parental genotypes. The F1 hybrid genotypes were filtered to leave only those with MAF >= 0.05, leaving 26736 SNPs for further analysis.56. Population structure analysis was carried out for F1 hybrid genotypes using smartpca software 57.We performed phylogenetic analysis for all parental lines using a neighbor-joining statistical method, whereas a bootstrap method was used to test for phylogeny (200 bootstraps). Phylogenetic analysis was carried out using MEGA software (version: 6.06)58. We found that the phenotype distributions of some traits in our phenotype datasets were highly skewed or bimodal. Therefore, python package WarpedLMM (version: 0.21)59 was used to perform phenotype normalization to ensure a Gaussian distribution of the phenotype residues before further GWAS analysis.Mixed linear models have been used in GWAS to control for population structure and familial relationships. One important assumption for mixed linear models is that the phenotype residues have a Gaussian distribution; any deviation from this assumption may cause spurious signals and reduce power40. To solve the first problem, we used a mixed linear model to control for population structure and close relationships among F1 hybrids. To solve the second problem, we used the forward-selection resampling GWAS method (based on a multiple loci model) instead of the single locus model used in traditional GWAS41. First, we randomly selected 80% of all samples from the total dataset without replacement to form a new sub-dataset. This selection procedure was repeated 300 times to form 300 sub-datasets. GWAS using a mixed linear model was performed iteratively for each sub-dataset, after which the SNP with the lowest P-value, provided that it passed the significance threshold, was added as a covariate for the next round of GWAS. This forward-selection GWAS procedure was repeated until no additional SNP passed the significance threshold. After finishing the GWAS analysis for all sub-datasets and averaging the results across all identified genetic models, a resample model inclusion probability , representing the model inclusion probability in 100 forward-selection resampling GWAS analyses, was assigned to each identified SNP. Those SNPs meeting the empirical RMIP threshold of 5 were identified as significantly correlated SNPs. GWAS analysis was performed using all 4 inheritance models: additive, dominance, recessive, and over-dominance. The additive inheritance model was utilized as in traditional GWAS . For dominance and recessive inheritance models, heterozygotes (Aa) were coded the same as either the homozygous genotypes of major alleles (AA) or homozygous genotypes of minor alleles (aa). The over-dominance model was utilized by recoding the heterozygote to 1 and both homozygotes to 0. Among the four RMIPs derived from these inheritance models, the biggest one was used for further analysis. To reduce the redundancy of association signals, we merged SNPs located less than 800 kb apart and showed correlations by linear regression analysis. GWAS was performed using R package ‘GenABEL’ (mmscore function)61. The genome-wide significance threshold for each GWAS analysis was determined by 300 permutation tests at a false discovery rate (FDR) lower than 0.05 using the Benjamini and Hochberg method62.To obtain a deep understanding of heterosis in hybrid rice, we separated each trait into three categories, F1, BPaV, and SCA, and identified genetic mechanisms underlying these trait categories by GWAS analysis. F1 represents the original phenotype values of the F1 hybrids. BPaV represents the better paternal values of the F1 hybrids , after which the total variance explained was estimated as the residual sum of squares by fitting all filtered QTLs after removal of family effects (variance explained by the top 10 genomic PCs).65. Dominance effects were assessed by recoding the three genotypes , whereas additive effects were assessed by recoding the three genotypes as 0, 1, and 2. Dominance and additive effects were fitted simultaneously in the linear regression model, and the top 10 genomic PCs were added as covariates to control for population structure. We used the following d/a criteria judged by Stuber et al.66 to define the QTL effects: additive = ; dominance =  or two homozygotes ). If any of these three groups had less than 15 samples, the QTL was placed into the two-genotype group; otherwise, it was placed into the three-genotype group. For two-genotype QTLs, we directly compared the average phenotype values of both two genotype classes. A two-genotype QTL was defined as hetero-superior if the average performance of its heterozygotes outperformed that of its homozygotes in the F1 hybrids; otherwise, it was defined as homo-superior. For three-genotype QTLs, we used a linear regression model to assess dominance/additive (d/a) effects by Plink software 67.We used Tajima’s D to find genomic regions under selective pressure in the 14 male sterile lines and 39 restorer lines, respectively. To include enough polymorphic sites for robust analysis results, we used a 240-kb sliding window size (containing approximately 15 polymorphic sites) with a 20-kb step size. A QTL was defined to be under selective pressure if it overlapped with any genomic region below the 10th percentile of Tajima’s D in either male sterile lines or restorer lines. Calculation of Tajima’s D was performed using Variscan software (version 2.0)Supplemental FileDataset 1Dataset 2Dataset 3


A genetic risk score could be beneficial in assisting clinical diagnosis for complex diseases with high heritability. With large-scale genome-wide association (GWA) data, the current study constructed a genetic risk model with a machine learning approach for bipolar disorder (BPD). The GWA dataset of BPD from the Genetic Association Information Network was used as the training data for model construction, and the Systematic Treatment Enhancement Program (STEP) GWA data were used as the validation dataset. A random forest algorithm was applied for pre-filtered markers, and variable importance indices were assessed. 289 candidate markers were selected by random forest procedures with good discriminability; the area under the receiver operating characteristic curve was 0.944 (0.935–0.953) in the training set and 0.702 (0.681–0.723) in the STEP dataset. Using a score with the cutoff of 184, the sensitivity and specificity for BPD was 0.777 and 0.854, respectively. Pathway analyses revealed important biological pathways for identified genes. In conclusion, the present study identified informative genetic markers to differentiate BPD from healthy controls with acceptable discriminability in the validation dataset. In the future, diagnosis classification can be further improved by assessing more comprehensive clinical risk factors and jointly analysing them with genetic data in large samples. An accurate risk score model has substantial benefits in assisting the early screening of diseases, patient management, and clinical diagnosis. In addition, a risk score model has been applied to the prognosis prediction for complex traits, such as cardiovascular diseases1456Although many GWA studies have been conducted for heritable traits, only a few susceptible loci are reproducibly reported, with a small effect size between 1.2 and 2.08The RF is an ensemble-based machine learning method that uses multiple classification and regression trees as classifiers. After taking the majority vote over all classifiers, the RF method combines information across all trees to reveal variable importance. It can assess associations and interactions simultaneouslyIn the current study, we focused on a complex psychiatric trait, bipolar disorder (BPD) with a high heritability of around 0.6 to 0.8182021824In the present study, we used the RF-based method to construct a genetic risk prediction model for BPD, using pre-screened potentially associated markers in large-scale GWA datasets. The procedures are as follows. First, the RF method was used to select important variables as candidate risk markers in a BPD GWA dataset from the Genetic Association Information Network (GAIN). Second, the multivariable logistic regression with variable-selection methods was used to further select a smaller optimal subset of the variables from all candidate risk markers. We could then build risk score models using the identified optimal markers for the GAIN-BPD dataset. Third, to estimate the performance of the risk score models, leave-one-out cross-validation was performed for internal validation. We also used the other BPD-GWA dataset, Systematic Treatment Enhancement Program (STEP), as an external validation data. Finally, we performed a gene sets analysis to uncover the underlying biological mechanisms for those loci that were identified as the candidate risk markers.The accuracy of the RF procedure was evaluated in the GAIN training set created during the forest growing process. The accuracy of the RF classification in the GAIN data was 0.939 in controls and 0.852 in BPD patients. We ranked markers based on values of the two indices, the Gini Index (GI) and the conditional variable importance (VI) from the RF procedure. Because the two indices did not completely agree with each other, we used the union markers of the top ranked 200 in each index. As The genetic risk score based on this final prediction model was calculated for each individual from accumulating numbers of the risk alleles and weighted by the beta regression coefficient. The risk scores among all participants were ranged from 143.8 to 228.4 in the GAIN dataset, with a mean of 175.4 in the controls and 191.3 in the BPD patients. To find an optimal cutoff point, we used the Youden Index to obtain the risk score cutoff as 184, and the corresponding sensitivity and specificity for BPD were 0.777 and 0.854, respectively . The likWe then used leave-one-out cross-validation to conduct internal validation for classification accuracy . The preALK, TACR1, LRP1B, GALNT17, NAV2, ODZ4, RAD51L1, KTN1, and CACNG2.We performed the same set of analyses using STEP data as the training dataset, and the GAIN data as the validation. The results are displayed in Significantly enriched gene-sets were identified for these mapped genes in the two GWA datasets of BPD. k-nearest neighbour classification, RF is often applied in biomedical research with different data sources, such as gene expression30It is a common interest to explore the usage of genetic findings for heritable complex traits. There is an absence in the literature of a risk score model based on genetic information for the diagnosis of BPD. Non-replication across datasets is often observed, especially when focusing on specifically significant markers. Hence, using extremely significant markers in one sample to construct a genetic risk model to apply to other samples might not produce good prediction accuracy. On the other hand, informative genetic markers, which are selected by methods of machine learning, have been used for the classification of outcomes or for predicting the risk of developing diseases, such as early detection of prostate cancerDiagnoses of psychiatric disorders often largely depend on clinical interview rather than biomarkers. With the RF procedures, the 289 candidate risk predictors in the GAIN dataset perform well with an AUROC of 0.944 and a 0.702 AUROC in the validation dataset. Moreover, high sensitivity and specificity are also observed using the more parsimonious 121 optimal markers and the risk score, with acceptable predicted error rates less than 0.2 in leave-one-out cross-validation. Without the RF procedures, if we selected the same 289 candidate predictors based on p-values significance in the GAIN data to estimate the discriminability in the STEP dataset, the AUROC slightly dropped to 0.686 (data not shown). In the literature, some risk score models were built using genetic information in aid of improving disease classification for complex traits, without satisfactory prediction power. For instance, Golan and colleagues (2014) used the random effect approach and reported the discrimination ability with an AUROC of 0.62 for BPD patients from the Wellcome Trust Case Control Consortium datasetIt is commonly observed that the accuracy of the genetic prediction model is reduced in external validation samples33ODZ4TACR1KTN1CACNG2ODZ4KTN1 gene in both brain and blood tissue40We ran both GWA datasets as the training and the other as the validation dataset for model construction. In either scenario, a very similar classification performance is observed, suggesting the stability of current procedures. However, we also noticed that there were no overlapping markers selected by RF in the two datasets as candidate risk markers. The agreement increased in gene levels across both datasets, where the same 9 genes are mapped in the two datasets. It may be intuitive, as genetic markers identified are often not causal variants, but rather the proxy for real causal variants. Therefore, the agreement may be the least in marker level, and the increase in gene and pathway levels, especially when heterogeneity exists among datasets. The 9 genes contained both sets of the candidate risk markers, and many studies have indicated that some of these genes are associated with BPD or brain function, such as There were some limitations in the present study. Although risk score models have been used to capture genetic effects from large-scale GWA studies, the power of discrimination was, however, inadequate in previous studies. Dudbridge and colleagues (2013) indicated that the power of polygenic score might be sufficient to use about 2,000 cases and controls, respectivelyIn conclusion, we successfully used a machine learning approach to extract informative genetic markers for the construction of a risk score model. Our results indicated a fair discrimination ability for BPD patients with AUROCs of around 0.70 in the external validation datasets. Integration of more comprehensive risk factors from family and environmental data in larger samples is necessary to construct a more precise and applicable risk score model for BPD, to assist with clinical diagnosis in the future.The study design and analysis flow chart are displayed in https://dbgap.ncbi.nlm.nih.gov/aa/wga.cgi?login=&page=login)https://www.nimhgenetics.org/available_data/bipolar_disorder/)24We used two individual GWA datasets of BPD in the Caucasian populations, the GAIN (www.hapmap.org). Well-imputed SNPs had squared correlations ≥0.30 between imputed and true genotypes, which were suggested by MACH. After removing markers with minor allele frequency (MAF) less than 1%, the number of well-imputed SNPs was 2,238,297 and 2,109,280 for the GAIN and the STEP datasets, respectively. In total, there were 1,992,730 well-imputed SNPs overlapped in the two datasets.Because the two GWA studies used different genotyping platforms, we imputed all the autosomal SNPs for the two GWA datasets based on those genotyped SNPs that passed quality control, to obtain the maximal number of common SNPs for the construction of prediction models for the two datasets. We applied Markov Chain Haplotyping (MACH) 1.0To construct the genetic prediction model for BPD, we first performed association analyses with the additive model for 1,992,730 well-imputed SNPs using PLINK versions 1.07i.e. 19,701 candidate SNPs in the GAIN dataset). The results from the growing of ensemble trees as a forest could provide a list of important variables for disease outcome. The RF procedures were performed using the Random Jungle packageTwo-thirds of the subjects in the GWA dataset were taken as the training set using the bootstrap procedure, and the remaining subjects were treated as the test set.Second, is the splitting step. A random subset of markers was chosen from all candidate markers without replacement. The size of each marker subset was equal to the square root of numbers of all candidate markers. The decrease in impurity for all markers was then calculated. The definition of the decrease in impurity was detailed elsewherend splitting step was repeated until the tree is grown with its largest extent in the tree growing step.The 2Steps 1 to 3 were repeated to grow 5,000 classification trees to build a forest.The prediction error of particular markers was estimated by permutation procedure from the test set.Two indices of the RF procedures were used for the selection of relevant risk predictors, the GI and the VI. The GI represents the total decrease in impurity of the whole dataset by summing the probability of each risk predictor being chosen multiplied by the probability of a mistake in categorizing a subset. The VI means the decrease in accuracy for every predictor. To avoid the bias induced by including highly correlated candidate markers such as SNPs in LD, we used the conditional permutation scheme in the tree building procedureTo select informative risk predictors for model construction, we used the RF method for classification and building regression trees. All candidate SNPs were used to build a training model  to select the optimal predictors and to obtain p-values, odds ratios (OR), and 95% CI. The genetic risk score for each individual was calculated by summing across all predictors in the model using the numbers of risk allele multiplied by the beta regression coefficient of each marker. The highest Youden IndexWe examined the performance of the classification models by several indices. First, the discrimination capability of the established prediction model was assessed with the receiver operating characteristic (ROC) curve, and an AUROC was calculated. The ROC curve was plotted by false-positive rate versus sensitivity measure. The goodness of fit for each prediction model was assessed by the Hosmer-Lemeshow test, which calculates the difference between the predicted and the observed risk. Leave-one-out cross-validation was performed for internal validation to obtain a bias-corrected estimation of error rate in prediction. The STEP GWA dataset was used as external validation for the prediction models. Statistical analyses in this stage were performed with SAS version 9.2 .http://www.broadinstitute.org/gsea/msigdb/annotate.jsp) to examine the common processes or the underlying biological gene sets of the selected candidate genese.g. canonical pathways, KEGG, Biocarta and Reactome). In total, 3,100 collections of gene sets were available, which includes 45,956 unique genes. Enriched gene sets were identified using the hypergeometric method, with the false discovery rate less than 0.01We used the Molecular Signatures Database .Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.


Bayesian mixture models in which the effects of SNP are assumed to come from normal distributions with different variances are attractive for simultaneous genomic prediction and QTL mapping. These models are usually implemented with Monte Carlo Markov Chain (MCMC) sampling, which requires long compute times with large genomic data sets. Here, we present an efficient approach (termed HyB_BR), which is a hybrid of an Expectation-Maximisation algorithm, followed by a limited number of MCMC without the requirement for burn-in.To test prediction accuracy from HyB_BR, dairy cattle and human disease trait data were used. In the dairy cattle data, there were four quantitative traits  measured in 16,214 cattle from two breeds genotyped for 632,002 SNPs. Validation of genomic predictions was in a subset of cattle either from the reference set or in animals from a third breeds that were not in the reference set. In all cases, HyB_BR gave almost identical accuracies to Bayesian mixture models implemented with full MCMC, however computational time was reduced by up to 1/17 of that required by full MCMC. The SNPs with high posterior probability of a non-zero effect were also very similar between full MCMC and HyB_BR, with several known genes affecting milk production in this category, as well as some novel genes. HyB_BR was also applied to seven human diseases with 4890 individuals genotyped for around 300 K SNPs in a case/control design, from the Welcome Trust Case Control Consortium (WTCCC). In this data set, the results demonstrated again that HyB_BR performed as well as Bayesian mixture models with full MCMC for genomic predictions and genetic architecture inference while reducing the computational time from 45 h with full MCMC to 3 h with HyB_BR.The results for quantitative traits in cattle and disease in humans demonstrate that HyB_BR can perform equally well as Bayesian mixture models implemented with full MCMC in terms of prediction accuracy, but with up to 17 times faster than the full MCMC implementations. The HyB_BR algorithm makes simultaneous genomic prediction, QTL mapping and inference of genetic architecture feasible in large genomic data sets.The online version of this article (doi:10.1186/s12864-016-3082-7) contains supplementary material, which is available to authorized users. Genomic prediction of genetic merit, using SNP markers, is now routinely used in animal and plant breeding to identify superior breeding individuals and so accelerate genetic gain –3. GenomGenomic predictions are often implemented using linear prediction models, especially best linear unbiased prediction (BLUP) or Genomic BLUP (GBLUP), which assume that all the SNPs contribute small effects to the trait and these effects are derived from a normal distribution , 4, 9. WTo address these problems, Bayesian mixture models  , 12–15 aP < 5*10−8) are used. This method of analysis has three limitations:1) The effect of those SNPs declared significant is usually over-estimated; 2) multiple SNPs in linkage disequilibrium with the same QTL may show an association with the trait leading to imprecision in mapping the QTL; 3) many QTL are not detected at all because no SNP reaches the stringent P-value for association with the trait. By comparison, Bayesian mixture models fit all SNPs simultaneously by treating the SNP effects as random effects drawn from a prior distribution. For example, the BayesR model has been implemented for QTL detection in the dairy cattle genome and for human disease traits ). Following the derivation steps of Kemper et al. σg2 , we evaluated the mean of the AUC for each disease shown in Table σg2), but just 3 SNPs with large effects (the variance 0.01σg2). These numbers demonstrated the polygenic architecture of BD. On the contrary, for T1D, there was relatively smaller number of SNPs  with small effects but many more SNPs  with large effects. The proportion numbers from Fig. σg2) controlled the polygenic architecture of the diseases BD , CAD , HT , and T2D . For these diseases, the mixture model of BayesR and HyB_BR did not have much advantage. However, relatively larger proportions of SNPs with moderate effects (the variance 0.001σg2) existed for the traits RA  and T1D. For these two traits controlled by major genes, BayesR and HyB_BR gave substantially greater accuracy than GBLUP, which explained the results for prediction accuracy (Table The inferred genetic architecture was different for each of the seven diseases Table . For exacy Table .Table 11σg2) but appeared to systematically detect more SNPs in the proportion of small variance (the variance 0.0001 * σg2), similar to the results observed for the comparison of BayesR and HyB_BR in in dairy cattle data  and the higher accuracy from MCMC implementations in a hybrid scheme. Our accuracies of genomic prediction for complex traits in human and cattle from HyB_BR are almost identical to those from the full MCMC implementation of the Bayesian mixture model, with a 10 fold or greater reduction in computing time required.For the pure MCMC algorithm, the burn-in stage can account for up to 50 % of the total running time. One of the key advantages of HyB_BR is that the EM module effectively replaces the burn-in cycles that are usually required for MCMC. Based on the starting point from EM , the running time of HyB_BR can be much reduced.The pure EM algorithm, EmBayesR  has beenO(mn) iterations), is greater than BayesR by full MCMC. And when implemented with the speed-up scheme described in the methods, computational time can be reduced even further, by sampling a reduced set of SNPs in the MCMC module, apparently with no loss of accuracy . Second, the prediction accuracy of HyB_BR is comparable to BayesR in all cases including dairy cattle and human disease prediction shown in Tables HyB_BR has three advantages. First, as the size of genomic data increases, the computational efficiency of HyB_BR without burn-in stage  for each SNP in front of EM iterations. In detail, the calculation of tr(E− 1ZiZi'E− 1PEV) requires the time complexity of T: if > 0.9), which is applicable for the current data. However, it’s uncertain whether or not such a threshold is suitable for other types of data.While HyB_BR performs well with computational efficiency and robust prediction accuracy, there are at least still two strategies that could be used to further improve efficiency. There is one key part of EM module that consumes running time and memory: the calculation of O(mn) but under different mixture models. In detail, BSLMM assumed a large proportion of SNPs with small effects (under BLUP models), while others had large effects . Due to limited number of SNPs implemented for MCMC sampling (large proportion of SNPs are under GBLUP models), BSLMM could be computationally efficient. However, compared with the mixture of four normal distributions by BayesR which provided great flexibility with respect genetic architecture, the flexibility of BSLMM with respect to different genetic architectures required further investigation. Another algorithm is BOLT-LMM, which has been developed mainly for the association studies. BOLT-LMM incorporated Bayesian mixture models to improve the power of GWAS with appealing outcomes. Instead of MCMC sampling, BOLT-LMM implemented iterative conditional expectation (ICE) algorithm on a mixture of two normal distributions to improve the computational speed with the approximated computational complexity O(mn). There could be three limitations with this method: 1) ICE algorithms did not account for the PEVs from all other SNP effects during the estimation of current SNP effect. On practical data sets, ICE could lead to the loss of prediction accuracy. BOLT-LMM introduced LD score regression technique to calibrate the prediction errors. However, since the calibrating factor was constant across all the SNPs (the prediction error variance regarding each SNP differs according to our equation (E− 1ZiZi'E− 1PEV)), such calibration scheme seem not to be effective to solve the problem. 2) The leave-one-chromosome-out scheme implemented in BOLT-LMM might perform well for GWAS but not be suitable for simultaneous genomic prediction. 3) BOLT-LMM treated each SNP effect as a fixed effect for the association statistics. This combined with the stringent significance threshold for multiple testing, leaded to the over-estimation for SNP effects. Another efficient method for genomic prediction termed MultiBLUP [HyB_BR has some features in common with other mixture methods such as BSLMM , and BOLultiBLUP  introducIn summary, HyB_BR is a computationally efficient method for simultaneous genomic prediction, QTL mapping and inference of genetic architecture. The hybrid scheme of MCMC and EM decreases computational time by a factor of at least 10 fold with no reduction in prediction accuracy. The HyB_BR algorithm makes simultaneous genomic prediction, QTL mapping and inference of genetic architecture feasible in extremely large genomic data sets including whole genome sequence data.


Triticum aestivum L.) impedes anthers inside the floret, making it largely an inbreeder. For hybrid seed production, high anther extrusion is needed to promote cross pollination and to ensure a high level of pollen availability for the seed plant. This study, therefore, aimed at the genetic dissection of anther extrusion (AE) in panels of spring (SP), and winter wheat (WP) accessions by genome wide association studies (GWAS). We performed GWAS to identify the SNP markers potentially linked with AE in each panel separately. Phenotypic data were collected for 3 years for each panel. The average levels of Pearson's correlation (r) among all years and their best linear unbiased estimates (BLUEs) within both panels were high (r(SP) = 0.75, P < 0.0001;r(WP) = 0.72, P < 0.0001). Genotypic data  included 12,066 and 12,191 SNP markers for SP and WP, respectively. Both genotypes and environment influenced the magnitude of AE. In total, 23 significant (|log10(P)| > 3.0) marker trait associations (MTAs) were detected . Anther extrusion behaved as a complex trait with significant markers having either favorable or unfavorable additive effects and imparting minor to moderate levels of phenotypic variance (R2(SP) = 9.75−14.24%; R2 (WP) = 9.44−16.98%). All mapped significant markers as well as the markers within their significant linkage disequilibrium (r2 ≥ 0.30) regions were blasted against wheat genome assembly (IWGSC1+popseq) to find the corresponding genes and their high confidence descriptions were retrieved. These genes and their orthologs in Hordeum vulgare, Brachypodium distachyon, Oryza sativa, and Sorghum bicolor revealed syntenic genomic regions potentially involved in flowering-related traits. Moreover, the expression data of these genes suggested potential candidates for AE. Our results suggest that the use of significant markers can help to introduce AE in high yielding varieties to increase cross fertilization rates and improve hybrid-seed production in wheat.Hybrid wheat breeding is gaining prominence worldwide because it ensures higher and more static yield than conventionally bred varieties. The cleistogamous floral architecture of wheat ( In many crops, hybrids have almost completely replaced the conventionally bred varieties because of their potential of higher and more stable yields even in marginal environments   was described in Muqaddasi et al. , arranging the accessions as a randomized complete block design . The individual plot size was 1 × 1.5 m, and each plot was split into four rows spaced 0.20 m apart. Standard agronomic wheat management practices were applied.The spring wheat panel consisting of 111 accessions from the Genebank of IPK in Gatersleben  was scored on field in both panels 5–10 days post-anthesis for the years 2013, 2014, and 2015 by observing the anthers retained inside the four pairs of primary and secondary florets sampled from the central portion of four spikes per plot. For years 2015 and 2016, AR was scored by taking 10 spikes per plot, harvested 5–10 days post-anthesis and held at −20°C until analysis in the laboratory. Field and laboratory based AR data (2015) were compared to check the usefulness of both methods. Anther extrusion was calculated by subtracting the number of retained (non-extruded) anthers from 24  as described in Muqaddasi et al.  applying the “Mixed models REML” module and the “Linear mixed models” function. A Pearson product moment correlation among the growing years and BLUEs was also calculated. The repeatability among the replicates (R) and heritability (H2) among the years were calculated from the individual variance components as nE is the number of environments and nR the number of replicates , assuming fixed genotypic effects. The calculations were performed using GenStat http://www.traitgenetics.com). The initial number of polymorphic loci was 13,006 for both panels. The SNP-chip data is available at digital object identifier (DOI) http://dx.doi.org/10.5447/IPK/2017/4. This DOI was created with e!DAL  based on SNP genotypes in software R Team, . The firK) as coefficient of co-ancestry  between all pairs of accessions in each panel individually by using GenStat v16.Assuming that the accession share some degree of relatedness, a genetic variance-covariance kinship matrix  was assumed to arise from a normal distribution as ~N which imposed a genetic variance-covariance structure. Genetic relatedness (structure) among accessions was considered by assuming the random genotype effect log10(P)| > 3.0 was set in GenStat v16 for the detection of significant MTAs. The MTA analysis was performed separately for each panel based on BLUEs. Observed vs. expected |log10(P)| value distributions were displayed in the form of quantile-quantile (qq) plots. For the set of markers unlinked to an AE-QTL, the |log10(P)| values would be expected to be uniformly distributed along the diagonal, however, extremely large deviations are indicative of spurious associations , and positive ones an increase . For the bi-allelic SNP markers the effects were related to the respective allele with minor allele frequency at each locus. TASSEL v3.0  explained by individual markers.Assuming the genetic relatedness among accessions, the following mixed model for MTA analysis on BLUEs dataset with SNP markers was used:v16 and R  vs. map distances in centiMorgans (cM).By using a set of mapped SNP markers  genome-wide linkage disequilibrium (LD) was studied in both panels. Intra-chromosomal and genome-wide quantification and graphical representation of LD heat maps and intra-chromosomal LD decay were accomplished with GenStat  R Team,  by plottr2 ≥ 0.30. Thus, we extracted the flanking sequences of all the markers from wheat 90K database  and blasted . All the markers sequences were blasted in Geneious v9.1.5 . Furthermore, the wheat transcript IDs of all the genes in significant LD regions were given in http://www.wheat-expression.com to retrieve their expression profiles in above-ground plant tissues at log2 transcripts per million (tpm) scale  = 0.81, P < 0.0001; r(WP) = 0.85, P < 0.0001)  was scored for 207 wheat accessions (111 spring and 96 winter) and showed a wide range of variation among accessions. The habit of growth, country of origin and AE scores of all 207 accessions are given in Table ) Figure . The lab) Figure . The obsP Figure , and theThe imposition of minor allele frequency (MAF) threshold of 5% reduced the SNP marker set to 12,066 markers for SP and 12,191 for WP, of which 10,578, and 10,649 had known map locations, respectively  assessment was performed using adjacent (pair-wise) SNP loci which revealed that LD decayed rapidly with increasing genetic map distances. The LD analyses of the chromosomes harboring the markers significantly associated with the AE Figures , S4 showA PCA based test for the existence of clustering among accessions for both panels is illustrated in Figure log10(P)| > 3.0) were identified in GWAS analyses  ranging from 9.75 to 14.27%. The significant MTAs of SP were detected on chromosomes 2B, 3A, 3B, 6A, 7A, and 7B (Table 10(P)| values, indicated that the model we used was sufficiently stringent to control for false positives  were identified for AE by using a mixed linear model  revealed 26 and 52 distinct markers in SP and WP, respectively. The corresponding orthologous genes/regions to these SNP markers were retrieved from wheat, barley, Brachypodium distachyon, sorghum and rice. Tables Analysis of all the significant markers and the markers in significant LD regions  (Tables r2 ≥ 0.30) revealed putative genes which could be directly or indirectly involved in AE in both panels.We extracted the wheat transcript IDs in significant LD regions and retrieved the gene expression data of above-ground tissues from  Figures , 7. One ) Tables . The genAnther extrusion (AE) was scored for a total of 207 wheat accessions including 111 spring (SP) and 96 winter (WP) over the period of 3 growing years which resulted in broad sense heritability values of 0.84 for SP and 0.65 for WP. Anther extrusion showed a strong phenotypic variation among accessions in both panels. The repeatability and broad sense heritability values for AE in both SP and WP complemented previous reports based on various wheat panels and different environments  analysis resulted in extremely low R2(SP) = 9.75−14.24%; R2(WP) = 9.44−16.98%) for individual SNPs.Anther extrusion in our study behaved as a quantitative trait in both SP and WP; controlled by the concerted action of several loci and explaining a minor to modest level of phenotypic variance  and five  QTL regions, respectively. Most studies published on AE are linkage-mapping studies . Skinnes et al. (R2 = 18.3%). Similarly a WP-QTL on chromosome 6B (71.18–72.29 cM) imparted an average of 11.73% of phenotypic variation. Buerstmayr and Buerstmayr , represented by significant SNP “s et al.  detectederstmayr  detectedNevertheless, it is important to keep in mind that all recent reports suggest an extremely complex nature of AE which warrants that the AE is controlled by many loci, mostly small effect, contrary to what was initially reported that AE is controlled by very small number of genes (Sage and De Isturiz, Brachypodium distachyon, rice and sorghum. The annotated functions of several genes suggested that the proteins they encode can be important components of flowering and reproduction related traits, for example, D111/G-patch domain-containing protein (Quiapim et al., We found several orthologous genes in close wheat relatives i.e., barley, Hybrid wheat breeding is a promising strategy to break the yield barriers (Muhleisen et al., QM performed the data and genome-wide association analyses and prepared the manuscript. JB participated in data analysis. AB, KP, and MR participated in the experimental design. MR conceived the idea and participated in the interpretation of results and preparation of manuscript. All authors read and approved the final 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.