Hypolimnas bolina. Through linkage mapping, we first identified a genomic region that was necessary for males to survive Wolbachia-induced male-killing. We then investigated the genomic impact of the rapid spread of suppression, which converted the Samoan population of this butterfly from a 100∶1 female-biased sex ratio in 2001 to a 1∶1 sex ratio by 2006. Models of this process revealed the potential for a chromosome-wide effect. To measure the impact of this episode of selection directly, the pattern of genetic variation before and after the spread of suppression was compared. Changes in allele frequencies were observed over a 25 cM region surrounding the suppressor locus, with a reduction in overall diversity observed at loci that co-segregate with the suppressor. These changes exceeded those expected from drift and occurred alongside the generation of linkage disequilibrium. The presence of novel allelic variants in 2006 suggests that the suppressor was likely to have been introduced via immigration rather than through de novo mutation. In addition, further sampling in 2010 indicated that many of the introduced variants were lost or had declined in frequency since 2006. We hypothesize that this loss may have resulted from a period of purifying selection, removing deleterious material that introgressed during the initial sweep. Our observations of the impact of suppression of sex ratio distorting activity reveal a very wide genomic imprint, reflecting its status as one of the strongest selective forces in nature.Symbionts that distort their host's sex ratio by favouring the production and survival of females are common in arthropods. Their presence produces intense Fisherian selection to return the sex ratio to parity, typified by the rapid spread of host ‘suppressor’ loci that restore male survival/development. In this study, we investigated the genomic impact of a selective event of this kind in the butterfly  Hypolimnas bolina shifted from 100 females per male to near parity, through the evolution of a suppressor gene. In our current study, we investigate the hypothesis that the strength of selection in this case was so strong that the genomic impact would go well beyond the suppressor gene itself. After mapping the location of the suppressor within the genome of H. bolina, we examined changes in genetic variation at sites on the same chromosome as the suppressor. We show that a broad region of the genome was affected by the spread of the suppressor. Our data also suggest that the selection may have been sufficiently strong to introduce deleterious material into the population, which was later purged by selection.The sex ratio of the offspring produced by an individual can be an evolutionary battleground. In many arthropod species, maternally inherited microbes selectively kill male hosts, and the host may in turn evolve strategies to restore the production or survival of males. When males are rare, the intensity of selection on the host may be extreme. We recently observed one such episode, in which the population sex ratio of the butterfly  In 1930, Fisher noted that the strength of selection on the sex ratio was frequency dependent, echoing earlier findings of Düsing Wolbachia induced male-killing activity in the butterfly Hypolimnas bolina represents a compelling observation of intense natural selection in the wild. Female H. bolina can carry a maternally inherited Wolbachia symbiont, wBol1, which kills male hosts as embryos th century, with infected male hosts  being found in the Philippines but not in other localities tested. By the late 20th century, suppression of male-killing was found throughout SE Asia, but not in Polynesian populations where the male-killing phenotype remained active H. bolina were infected with male-killing Wolbachia, resulting in a sex ratio of around 100 females per male within the population The evolution of suppression of When strong selection occurs at a locus, it is expected to leave a genomic imprint beyond the target of selection, as a result of genetic hitch-hiking. A neutral (or even deleterious) variant that is initially present in the haplotype in which the favoured allele arose (i.e. is linked to the site of selection), will also increase in frequency Wolbachia. We then investigated the impact of the recent spread of the suppressor in Samoa on the pattern of variation around this region. To this end, we initially developed theory to predict the impact of suppressor spread on linked genetic variation. We then directly observed changes in the frequency of genetic variants surrounding the suppressor locus by comparing the pattern of genetic variation in H. bolina specimens collected in Samoa before (2001) and after the selective sweep (2006 and 2010). By examining post-sweep samples at two time points we were additionally able to track allele frequency changes following the initial sweep. The data revealed changes in the pattern of genetic variation over a 25 cM region surrounding the suppressor locus. We further suggest that the suppressor was probably derived by immigration, and that the sweep may have introduced deleterious material that was subsequently subject to purifying selection.In this paper, we first mapped a genomic region in SE Asian butterflies that was required for male survival in the presence of Hypolimnas bolina has 31 chromosomes and a total genome size of 435 MB Wolbachia induced killing was dominant, and potentially a single locus trait H. bolina orthologs obtained through Roche 454 transcriptome sequencing . The resulting F1 daughters (who inherited Wolbachia from their SE Asian mother) were then backcrossed to Moorea males to create a female-informative family for identification of loci linked to the suppressor. The absence of recombination in female Lepidoptera means that a SE Asia allele on any chromosome that is necessary for male survival will be present in all of the surviving sons of this female , but this allele will show normal 1∶1 segregation in her daughters 16: p<0.0001).aughters . InitialB. mori, and then confirmed as showing co-segregation with the original marker and as being associated with male survival, in the female-informative family. In this way, a suite of 12 suppressor-linked markers (A-L) were developed, all of which followed the presumed pattern of inheritance of the suppressor - that of presence in all 16 sons and half of the daughters. The remaining 9 non-suppressor-linked markers (M-U), representing 8 separate linkage groups, were developed to investigate potential genome-wide effects. Marker information and accession numbers are given in We then obtained an additional 11 markers in this linkage group. Candidates were identified initially via synteny to Wolbachia-infected Moorea (non-suppressor) females . 307 recombinant daughters were obtained, which were used to create a linkage map of the 12 suppressor-linked markers (data used to create linkage map in B. mori (60 = 9×10−19. Thus we posit that the suppressor lies between marker C at +8 (excluded by one recombinant) and marker G at +17 (excluded by two recombinants) - a region of approximately 10 cM. Our data also indicate that while this genomic region is necessary for male survival, presence of this locus was not always associated with male survival, with the number of surviving sons obtained being one quarter, rather than one half, of the number of daughters obtained in our cross (60 sons vs 307 daughters).A linkage map for this chromosome, the suppressor linkage group (SLG), was then constructed. The region required for male survival was identified by the exclusion of recombinants. This was achieved by examining the segregation of alleles from sons of the SE Asia x Moorea cross above that were mated to  B. mori . The sup B. mori . The proWolbachia and the frequency of suppression: as the suppressor spreads, the population sex ratio shifts towards 1∶1, thus reducing the selective pressure for further spread. We previously modelled the spread of the suppressor in this system using deterministic calculations Wolbachia-infected males lacking the S suppressor gene (i.e. those with genotype ss) being killed early in development. Thus the adult pool of male genotypes differs from the zygotic pool, and has a higher frequency of suppression than the adult female pool. Fisherian selection is then implicit in the model, with the suppressor increasing in frequency between the zygote and adult phase by virtue of being overrepresented in male hosts that contribute 50% of the genetic material to the next generation.Models of selective sweep dynamics commonly utilize a fixed selective coefficient. In contrast, the intensity of selection is dynamic in our system, as the benefit of rescuing a male relates to population sex ratio, which depends on the frequency of male-killing H. bolina, Wolbachia was initially at a 99% prevalence in females Ss), and to 25% frequency in the subsequent generation. Males that survive Wolbachia infection by carrying the suppressor are then induced to express another reproductive manipulation commonly employed by Wolbachia: cytoplasmic incompatibility (CI) against uninfected females Wolbachia to remain at or near fixation. As a consequence, selection on the suppressor is also maintained. Indeed fixation for Wolbachia in males and females is observed after the spread of the suppressor In the Samoan population of r = 0 (zero recombination with the suppressor). We elaborated the model of suppressor spread to quantify the expected effects on linked loci under the assumption that the suppressor and linked alleles were cost-free, that recombination occurred in males only, and that spread was occurring through an unstructured, panmictic population .The expected dynamics of the suppressor locus in this system is given in ss), half of the males that are heterozygous (Ss) for the suppressor, and none of the males that are homozygous (SS) for the suppressor. This partially dominant rescue mirrors the patterns of male survival in our mapping crosses, in which about 60 Ss males survive, compared to 150 Ss females . For simplicity we assume no other selective effects. This process allows us to track both gametic and genotypic frequencies through time.Given a set of genotype frequencies for males and females, we can derive the expected gametic frequencies , and assuming random mating we can calculate the frequencies of offspring genotypes in the next generation. We can then apply selection: we assume that the infection kills all males lacking the suppressor allele (AASS. The selected locus (r = 0) is observed to reach over 95% frequency within 10–15 generations, which is consistent with the observed rapid spread of the suppressor  within the linkage group, both in terms of LD with the suppressor locus , and locH. bolina on the island of Upolu, Samoa, through comparison of allelic profiles in the SLG before and after the spread of suppressor  not linked to the suppressor, which derived from 8 different linkage groups.We investigated the change in frequency of genetic variants associated with the spread of suppression of male-killing in ssor see . To thisssor see . HaplotySignificant changes in the allele frequency distribution between the 2001 and 2006 population samples were observed at 11 of the 12 markers along the chromosome identified above as carrying the locus necessary for male survival in SE Asian butterflies, spanning a region covering 25 cM . Only thST statistic for each locus in the SLG as a standardized magnitude of differentiation between the 2001 and 2006 population samples , and in this region allele diversity (AE) approximately halved between 2001 and 2006. Lower, but significant, FST was found over a 25 cM region surrounding the locus , but there was no overall change in allele diversity at loci situated further from the suppressor locus. Changes in nucleotide diversity between 2001 and 2006 echoed changes in allele diversity. Reductions in π were observed at the three loci that co-segregated with suppression (D–F), while there was little or no perturbation in overall diversity outside this region (1−exp[−t/2N]), with the standard deviation given by the square root of this measure. We use this formulation to examine the magnitude of change accountable for by drift between 2001 and 2006. We do this for the simplest cases, loci A, F, G and I, which cover 17 cM surrounding the suppressor locus, and are characterized by novel alleles in the 2006 sample. We make the conservative assumption that each allele is at the upper 95% confidence interval for its starting frequency, 0.0377, in 2001, and that there are 10 generations per year. Putting t = 50, p = 0.0377 and N = 500, it is improbable that change associated with drift between 2001 and 2006, could cause changes in allele frequency greater than 3 standard deviations, or 0.12. In each case, the alleles that have entered the population have attained frequency in excess of 0.2, suggesting that drift alone cannot explain the observed changes.Further evidence of the role of selection in driving the change in allele frequency on chromosome 25 derives from three sources: a) the magnitude of changes observed compared to those expected from drift processes, b) generation of LD in the 2006 post-suppressor spread population, and c) lack of significant changes in unlinked loci. The magnitude of changes expected under drift can be ascertained from the variance of a neutral Wright-Fisher process. The expected variance in allele frequency after The pattern of LD also reflected an episode of selection in this genomic region. Our model above predicted that LD between the suppressor-linked loci and the target of selection  would exist only in the very early phases of the sweep (10–20 generations), but that the sweep would create multiple local associations between closely linked loci that would be retained over longer periods  . In accoST was either zero or very low (FST<0.015) in this group of markers . Local LD was still observed, but, as expected from continued recombinational erosion, the extent of LD was confined to very tightly linked loci  collected in 2010 , we consider it likely that eN is considerably larger than this, and thus conclude that drift was unlikely to cause the loss of material observed. Furthermore, we note that loss of introgressed material occurred at two genomic locations that were not in LD with each other, again making chance sampling an unlikely source of the loss of material. Rather, we hypothesize that purifying selection against introgressed material is the most likely reason for the loss of swept alleles.We finally examined whether the loss of originally swept suppressor-linked alleles by 2010 could be explained by genetic drift. Using the model of Kimura  declined - the classical signature of a selective sweep. Three further features implicate the role of selection in altering allele frequency across this 25 cM region. First, the changes in allele frequency are too large to be accounted for by drift, even under conservative assumptions for population size and generation time. Second, LD is generated across this region, as predicted under a model of strong selection. Third, 9 markers unlinked to the suppressor linkage group showed no evidence of changes in the frequency of allele variants between 2001 and 2006, implying that demographic factors were not the major force driving changes in allele frequency.Our data identified a 10 cM genomic region on chromosome 25 of SE Asian While we observed changes consistent with the operation of selection over a very broad genomic area, the degree of change was less than that predicted from our model. This is true both of the magnitude of allele frequency change at loci located near the suppressor locus, and the breadth of the region of chromosome over which changes in allele frequency occurred. Our model, which presumes a panmictic model and no cost to carrying the suppressor, predicts the suppressor should fix , and that allele frequency changes should be observed chromosome-wide. In contrast, the swept allele at locus D (which lies within 5 cM of the target of selection) attains a frequency of just 0.67  in 2006 and 2010 samples. Further, we observed only very small changes in allele frequency at the most distant locus from the region containing the suppressor, locus L.Wolbachia again makes this a poor explanation for the failure of tightly linked loci to reach high frequency. Because it is necessary, it should become fixed in the population, and closely associated allele variants should in consequence attain very high frequency. A third possibility is that there is a cost to being homozygous for the suppressor mutation, either in both sexes, or in female hosts only. A cost such as this could prevent fixation of the suppressor allele, and thus also help account for the decreased magnitude of effect at loci tightly linked to the suppressor. If the suppressor allele reaches >0.75 frequency, then males lacking the suppressor would be sufficiently rare that the population sex ratio would be near parity. Biologically, costs to suppressor carriage may be directly associated with the suppression system itself. Modification of a sex determination gene, for instance, might rescue males but be deleterious in females, or when homozygous. Alternatively, costs may be associated with linked mutations. The presence of deleterious loci in linkage with the suppressor is supported by our observation that some material that had been initially swept into the population was lost between 2006 and 2010. Finer-scale investigation of this linkage group, especially within the region identified as required for male survival, is necessary to illuminate the precise dynamics that occurred during this episode of selection.We suggest there are three non-mutually exclusive explanations for this lack of fit with the model. First, the suppressor mutation in natural populations diffuses spatially following its initial arrival, and each generation of spatial diffusion is associated with a narrower local sweep. The principle impact of spatial diffusion will be to narrow the genomic region that is affected by selection compared to that predicted in a panmictic model, and to reduce the magnitude of change at loci far from the target of selection. For a locus 25 cM distant from the suppressor, association with the suppressor allele may last just one or two generations, such that changes in allele frequency occur only near the point of origin, and are diluted by absence of any selection on these loci in the majority of the species range. However, spatial diffusion represents a poor explanation for the lower than expected frequency of variants at tightly linked loci post-sweep, which are expected to maintain strong association during the spread of the suppressor across the island, as this occurs in about 10 generations. A second possibility is the involvement of other loci in the genome, as enhancers of suppressor action. Our data indicate that the genomic region in question is necessary for male survival, but do not rule out involvement of other loci in enhancing suppression. If other loci are involved, either as required elements or enhancers of male survival, this would slow suppressor spread, and might account for the narrowness of the sweep observed compared to model predictions. However, the requirement of the genomic region for male survival in the presence of de novo mutation. This may be an identical mutation to that found in SE Asia, or an alternative mutation in the same gene, which still confers suppression. Alternatively, there may be a suppression-conferring mutation in a different gene within the region identified as containing the suppressor.In our data, we observed concordance between the position of the suppressor ascertained in SE Asian butterflies, and the genomic region subject to selection during spread of suppression through the Samoan population of the butterfly. This observation has two possible interpretations. First, the suppressor mutation may have been introduced into Samoa by migration. Given that the suppressor is absent in the nearest island groups, American Samoa and Fiji, suppressor introduction would be associated with a long distant migrant. Second, the genomic region identified here may represent a hotspot for suppressor mutation, derived independently in Samoa by The presence of novel swept alleles at loci linked to the suppressor indicates that migration is the most parsimonious explanation for suppressor origin. Variants not present in the 2001 sample were observed to be the main ‘swept’ allele at 4 of the 11 loci at which significant change was detected . Future research should aim to establish the actual nature of the suppressor mutation in both Samoa and SE Asia through fine-scale genetic mapping. Such a project will allow the source of suppression on Samoa (migration or in situ mutation) to be clarified. Beyond this, it will reveal the actual target of selection in this system. It has been widely conjectured that the evolution of sex determination systems might occur in response to the presence of sex ratio distorting microbes H. bolina to obtain coding sequence from multiple loci across the genome. Following total RNA extraction from 1 male and 1 female adult H. bolina, mRNA library construction and sequencing using the Roche 454 sequencing platform (http://www.454.com), 450 bp reads were de novo assembled into contigs using the Newbler assembler to create the first set of Expressed Sequence Tags (EST) for H. bolina. The trimmed reads have been deposited as one male, and one female, partial transcriptome datasets in the NCBI SRA database, accession SRP045735.We utilized high-throughput sequencing of the transcriptome of H. bolina, the moth Bombyx mori was used as a proxy reference genome, this being the only available resource for Lepidoptera at the time of the study. There is a high level of synteny of gene location in the Lepidoptera B. mori were initially targeted and then retrieved from NCBI (http://www.ncbi.nlm.nih.gov). To determine putative H. bolina orthologs a local tBLASTx was then performed against the H. bolina EST set. Only genes that returned a single tBLASTx hit were included, reducing the likelihood of the inclusion of paralogs in our marker set. The orthologous H. bolina contigs were then translated into amino acid sequences using the ExPASY online tool (http://web.expasy.org/translate), with the sequence lacking mid-sequence stop codons chosen as the most likely translation. In a final test for paralogs, a reciprocal BLAST was performed of coding sequence from the orthologous H. bolina contigs as queries against the B. mori genome using the INPARANOID8 search tool (http://inparanoid.sbc.su.se/).In the absence of any annotated genome or transcriptome for H. bolina genes to be inferred using the B. mori genome. Through tBLASTx analysis of the B. mori coding sequence of the targeted gene against the B. mori WGS (Whole Genome Shotgun contigs) database in NCBI, exonic regions were identified . The translated orthologous H. bolina contig and the corresponding B. mori amino acid sequence were aligned using ClustalW Where present, intronic regions were targeted for marker development, as they are likely to have a higher degree of nucleotide diversity. Again, conservation of synteny in Lepidoptera genome organisation allowed the intron/exon boundaries in B. mori genes, and extrapolated to the H. bolina orthologous sequences, primers were designed for H. bolina that spanned introns of size 500–1000 bp (Bombyx size approximation). This size range was chosen to enable successful amplification of the intronic region during PCR. Marker optimisation was performed using three test H. bolina samples and successful PCR products were sequenced using Sanger technology.Once intron/exon boundaries were identified in H. bolina and determine markers in linkage with the suppressor locus, we crossed females of a butterfly population (the Philippines) that were Wolbachia-infected and homozygous for the male-killing suppressor allele (SS) to males from a Wolbachia-infected population  that lacked the suppressor (ss), to create suppressor-heterozygous Wolbachia-infected offspring (Ss)  .Ss females to be used to identify the linkage group  in which the dominant suppressor allele was carried. To this end, Ss females were crossed with ss males to produce the female-informative families. For inclusion in the SLG, markers linked to the suppressor locus are characterized by being present in all surviving sons of the Ss heterozygous mother, rather than the 50% expectation from Mendelian segregation with random survival. Initially each marker was sequenced in the F1 parents . In each case, SNPs were chosen that were heterozygous in the female and homozygous in the male – following the presumed pattern of the suppressor. These same SNPs were then scored in 16 male and 8 female F2 progeny. Once a marker had been found that was present in half of the daughters (following Mendelian inheritance) but all of the sons , further markers were developed for that same chromosome based on synteny with B. mori. A final suite of 12 markers that produced clean sequence and that spanned the suppressor-associated chromosome were developed to form the SLG.Recombination does not occur during female meiosis in the Lepidoptera H. bolina, and thus crosses of Ss males to ss females  allow a) mapping of genetic markers within a chromosome relative to each other and b) mapping of the suppressor within the linkage group, in terms of a region of the chromosome that is always present in surviving sons. To this end, the 12 linked markers were sequenced in the female F2 (n = 307) from one male informative cross  and a linkage map created using JoinMap  Recombination does occur in male www.qiagen.com), and the suite of 12 suppressor-linked markers amplified using PCR. Following Sanger sequencing of the amplicons through both strands, the resultant marker sequences were alignment in Codoncode (www.codoncode.com/). SNPs present within and between the population samples were then identified and scored for each individual butterfly. Using the SNP data  were collected from the Samoan island of Upolu. For each individual, DNA was extracted using the Qiagen DNeasy kit , Tajima's D, haplotype diversity (Hd)) for each marker for each time point were conducted in DnaSP (version 5) DNA polymorphism statistics and estimates of nucleotide diversity  female that was homozygous for the suppressor allele (SS) was crossed to a uninfected male that did not carry this allele (ss). To produce a female-informative family, Wolbachia-infected heterozygous daughters (Ss) from this pairing were in turn crossed to uninfected males lacking the suppressor. Because there is no recombination in female Lepidoptera, male survival is associated with inheritance of the linkage group carrying the suppressor, and suppressor-linked loci can be identified as those present in all surviving F2 sons (those marked with a cross die) but only 50% of F2 daughters. To produce a male-informative family, Wolbachia-infected heterozygous sons (Ss) from the original parental cross were crossed to infected females lacking the suppressor. Using this cross, members of the suppressor-associated linkage group were mapped relative to each other through the pattern of recombination in the F2 daughters. The location of the suppressor was ascertained as the genomic region that was present in all surviving F2 sons.(TIF)Click here for additional data file.S2 FigureResults of statistical testing for genotypic differentiation between population samples at loci in the linkage group carrying the suppressor. Significance denoted by colour: deep red – significant differentiation as measured at p<0.001; mid red – significant differentiation as measured at p<0.01; pink – significant differentiation as measured at p<0.05, all uncorrected for multiple tests.(TIF)Click here for additional data file.S3 FigureAllele frequency profiles of markers unlinked to the suppressor. Allele frequency changes for all 9 unlinked alleles (M-U) between 2001 (red) and 2006 (blue) at all 9 loci were not significant .(TIF)Click here for additional data file.S1 TableMarker loci information. Information of each of the 21  loci used in this study including gene annotation, linkage group and primers used. SLG: Suppressor Linkage Group; nt: nucleotides.(TIF)Click here for additional data file.S2 TableBasic haplotype polymorphism information and accession numbers.(TIF)Click here for additional data file.S3 TablePolymorphism statistics and nucleotide diversity estimates for the 12 suppressor-linked loci (A-L) for the 2001, 2006 and 2010 Samoan population samples. #: number.(TIF)Click here for additional data file.S4 TablePolymorphism statistics and nucleotide diversity estimates for the 9 unlinked loci (M-U) for the 2001 and 2006 Samoan population samples. Only SNPs were used in these analyses, indels where excluded. #: number.(TIF)Click here for additional data file.S5 TableST analysis of differentiation between 2001 and 2006 Samoan population samples at the nine unlinked loci.F(TIF)Click here for additional data file.S6 TableData generated for linkage mapping. Data for 307 daughters of the male-informative cross in the format required for Joinmap.(XLSX)Click here for additional data file.S7 TableGenotypes for each individual used in the study, for the 12 suppressor-linked markers. Each SNP is denoted using the IUPAC code. Missing data occurred where the sequence was not scorable for that individual.(XLSX)Click here for additional data file.S1 TextModelling the spread of the suppressor.(DOCX)Click here for additional data file.


Twenty-two loci for soybean SW and candidate genes conditioning seed development were identified; and prediction accuracies of GS and MAS were estimated through cross-validation and validation with unrelated populations.Glycine max) is a major crop for plant protein and oil production, and seed weight (SW) is important for yield and quality in food/vegetable uses of soybean. However, our knowledge of genes controlling SW remains limited. To better understand the molecular mechanism underlying the trait and explore marker-based breeding approaches, we conducted a genome-wide association study in a population of 309 soybean germplasm accessions using 31,045 single nucleotide polymorphisms (SNPs), and estimated the prediction accuracy of genomic selection (GS) and marker-assisted selection (MAS) for SW. Twenty-two loci of minor effect associated with SW were identified, including hotspots on Gm04 and Gm19. The mixed model containing these loci explained 83.4 % of phenotypic variation. Candidate genes with Arabidopsis orthologs conditioning SW were also proposed. The prediction accuracies of GS and MAS by cross-validation were 0.75–0.87 and 0.62–0.75, respectively, depending on the number of SNPs used and the size of training population. GS also outperformed MAS when the validation was performed using unrelated panels across a wide range of maturities, with an average prediction accuracy of 0.74 versus 0.53. This study convincingly demonstrated that soybean SW is controlled by numerous minor-effect loci. It greatly enhances our understanding of the genetic basis of SW in soybean and facilitates the identification of genes controlling the trait. It also suggests that GS holds promise for accelerating soybean breeding progress. The results are helpful for genetic improvement and genomic prediction of yield in soybean.Soybean (The online version of this article (doi:10.1007/s00122-015-2614-x) contains supplementary material, which is available to authorized users. Glycine max), rich in both protein and oil, is one of the most economically important crops. It accounted for approximately 68 % of world protein meal consumption and 57 % of world oilseed production during the past decades . As a yield component, seed weight (SW) is a complex and agronomically important trait in soybean. It is considerably attributed to seed size, which is an important character of soybean cultivars and affects the quality of many soy products for human consumption, such as soy sprouts, soy nuts, edamame, soy sauce, natto and miso , one of the ARF transcription factor family members that bind to auxin-responsive elements in the promoters of auxin-regulated genes, plays a central role in various auxin-mediated developmental processes including seed growing , AHK3 and AHK4  fulfill important roles in cytokinin-dependent endospermal and maternal control of embryo size. Triple mutant ahk2,3,4 showed increased cell number and cell size of the embryo, resulting in enlarged seed size , an ethylene responsive element binding protein and functioning in the floral and seed development . However, because of the limited recombination or insufficient maker density, the previously identified chromosomal regions associated with SW were usually not fine enough to access candidate gene(s) . A recent study indicated that the GmCYP78A10 gene, strongly associated with seed size in soybean, underwent artificial selection during early stage of soybean domestication  and genomic selection (GS) present promising prospects for genetic improvement of complex traits in crop species. GWAS with a population of unrelated lines and high-density single nucleotide polymorphism (SNP) markers is capable of identifying causal genes for a broad range of complex traits in different crops . This study enhances our understanding of the genetic architecture of SW and expedites the identification of genes conditioning SW in soybean. It demonstrates that GS can increase breeding efficiency and is also useful for genomic prediction of yield in soybean.Therefore, the objectives of this study were to (1) better understand the genetic architecture underlying SW in soybean, and (2) explore the potential of marker-based prediction as a new approach in soybean breeding. Twenty-two loci associated with SW and putative candidate genes with http://www.ars-grin.gov/), 92 % of the PIs are maturity group (MG) 0 and 8 % MG 00, and 91 % originated from Northern China. The detailed information about the 309 PIs was given in our previous publication , obtained from the USDA Soybean Germplasm Collection, were planted in single-row plots in a randomized complete block design with three replications at four environments: Aurora , Brookings  and Watertown  in South Dakota, USA. The plots were 3.05 m in length and 0.76 m in width (or row spacing), and 86 seeds were sown per plot/row. According to the GRIN (yijk = µ + gi + lj + (gl)ij + bk(j) + eijk, where µ is the overall mean, gi is the genetic effect of the ith genotype, lj is the effect of the jth environment, (gl)ij is the interaction effect between the ith genotype and the jth environment, bk(j) is the block effect within the jth environment, and eijk is a random error following N. Broad-sense heritability was calculated on an entry-mean basis as H2 = σg2/[σg2 + σgl2/k + σe2/(rk)], where σg2 is the genotypic variance, σgl2 is the genotype by environment interaction variance, k is the number of environments, r is the number of replications. Estimation of variance components was performed by the varcomp procedure in SAS version 9.3 , with all effects considered to be random. The likelihood-ratio-based R2 was calculated to estimate the proportion of total variation explained by the mixed linear model (MLM) containing all identified loci for trait as described by Sun et al. , and the seeds were dried in an air dryer. A sample of 100 cleaned seeds from each plot was randomly taken and weighed, and the data were presented as grams per 100-seed. The model for the phenotypic trait was n et al. .http://www.soybase.org/snps/index.php), and the imputation analysis was performed same as described above for the main association panel.The Illumina Infinium SoySNP50K BeadChip was used to genotype the population as described by Song et al. , and 42,r2) of alleles using R package synbreed . Only r2 for SNPs with pairwise distance less than 10 Mb in either euchromatic or heterochromatic regions was used to draw the average LD decay figure by R script using the equation described by Remington et al.  of genetic effect for each line were calculated using the R package lme4 , μ is the overall mean, X is the incidence matrix relating the individuals to the fixed marker effects α, P is the incidence matrix relating the individuals to the fixed principal component (PC) effects β, and Z is the incidence matrix relating the individuals to the random group effects u obtained from the compression algorithm. The random group effects u follows a multivariate normal distribution with mean 0 and variance–covariance matrix 2KVg, where K is the kinship matrix, and Vg is the genetic variance component. The random error term e follows a multivariate normal distribution with mean 0 and variance–covariance matrix IVe, where I is the identity matrix and Ve is the error variance component. GLM, compressed MLM and regular MLM could be achieved by set different level of compression as described by the manual of GAPIT. The first four PCs were involved in models as covariates according to Bayesian Information Criterion (BIC) test of the model fitness. The significance threshold for SNP-trait associations was determined by false discovery rate  <0.05 or P < 7.9 × 10−5.For the MLM analysis, the equation wasr) between the BLUPs of genetic effects and the GEBVs with the square root of the heritability , β is a m × 1 vector of marker effect and assumed random effect with Var[β] = Kσβ2, where m is the number of marker and K is the identity matrix , μ is the mean, βi is the fixed effect of the selected marker i, Xi is the marker genotype matrix of selected marker i, and e is the residual error. The GEBV of each individual j in validation set based on the selected markers was calculated as:l is the number of selected marker.For MAS by MLR method, different numbers of loci were selected from the 22 loci identified via GWAS through stepwise algorithm based upon Akaike information criterion (AIC), which was implemented using R package MASS (Venables and Ripley http://www.ars-grin.gov/cgi-bin/npgs/html/desc.pl?51015). They were SOYBEAN.EVALUATION.1MN63 (MN63), SOYBEAN.EVALUATION.1IL64 (IL64), SOYBEAN.EVALUATION.3IL83.2 (IL83.2) and SOYBEAN.EVALUATION.MS989 (MS989) (Supplementary file Table S1). Lines presented in the association panel were excluded from analyses, and thus the final population size was 270, 724, 192 and 425 for MN63, IL64, IL83.2 and MS989, respectively. The whole population of each panel was used for validation based on the marker effects estimated from the association panel. The prediction accuracies for these validations were simply estimated as the Pearson’s correlation (r), as no heritability was available for adjustment.Both GS and MAS were validated with four unrelated data sets taken from GRIN (r > 0.85 (P < 10−10), indicating high repeatability of the trait performance. The estimate of broad-sense heritability was 0.97, suggesting that the majority of phenotypic variation in soybean SW is attributed to genetic effects.The averaged SW over four environments showed a continuous distribution in the GWAS panel of 309 soybean PIs, with a wide range of variation from 7.3 to 23.6 g per 100-seed . The ANOVA indicated that effects of genotypes, environments and their interaction were significant (Supplementary file Table S2). The correlations of trait performance across environments were quite high, averaged r2 drop to half of its maximum value) at 326 kb in euchromatic region, while in heterochromatic region LD did not decay until 4285 kb .A total of 31,045 SNPs with minor allele frequency (MAF) ≥0.05 was used to GWAS for SW after quality control, resulting in a genome-wide marker density of 29 kb per SNP. On the SoySNP50K, however, markers were designed to unevenly distribute across chromosomal regions due to the substantial difference in recombination ratio between euchromatic and heterochromatic regions  and were 33.1 kb apart each other. The putative gene Glyma19g33421, identified close to the lead SNP Gm19_41013395_C_T (MAF = 0.27)  . On average, the individuals carrying the minor frequency allele of the lead SNP exhibited 1.9 g higher than those with major frequency allele in 100-seed weight . It was located 336 bp upstream of the transcript start site of a putative gene, Glyma10g28250, was found at 35 kb downstream of the lead SNP of SW11   and corresponded to an LD block with about 65 kb in length on Gm20. There were six putative genes located in this region , the prediction accuracies ranged 0.80–0.85 and 0.64–0.74 for GS and MAS, respectively, varying with the number of SNPs used for prediction . These panels represent a wide range of maturities (MG 000-VIII) and a large variation for SW . An approximately normal distribution was observed for SW in the panels except MS989 with a later maturity . The prediction accuracies of GS ranged from 0.63 for MS989 to 0.83 for 3IL83.2, 21 % averagely higher than that of MAS, which ranged from 0.42 for MS989 to 0.58 for 1MN63 . Additionally, many QTLs associated with seed size, a trait highly related to SW, have also been identified. These QTLs could be used to confirm the loci identified via GWAS, especially the hot ones. In this study, 22 loci associated with SW were identified. Each individual locus could explain a small proportion (<4 %) of phenotypic variance. The result demonstrated that soybean seed weight is a typical quantitative trait, genetically conditioned by many minor-effect loci. Of the identified loci, 15 have been previously reported at least once , we further decreased the number of candidate genes to eight for SW11 and five for SW22, respectively. The closest seed transcript to the lead SNP of the SW11 locus, Glyma10g28250, was predicted to encode a MYB61-like transcription factor. In Arabidopsis, MYB61 is required for mucilage deposition and extrusion during imbibition of seed coat   as well as cytokinin response factors (CRFs), which include a sub set of AP2 transcriptional factors . Therefore, it is conceivable that Glyma19g33421, encoding an AHP protein, might be involved in cytokinin-mediated seed mass regulation pathway in soybean. The SW21 locus was mapped to a region on Gm19 similar to 12 previously reported QTLs for SW or seed size related traits. The candidate gene, Glyma19g35180, putatively encodes an AUX/IAA family protein  was also carried out. We found that the prediction accuracy of GS varied among the panels with different groups of maturity , soybean cultivars with MG 000-IV accounted for over three-fourths of the U.S. soybean production in 2013. Therefore, GS with the marker effects estimated in this study hold a great potential in predicting soybean SW. Given SW is an important component of grain yield, the results are also useful for the genomic prediction and genetic improvement of soybean yield.In most of the GS or MAS studies, the training and validation populations are related, and cross-validation is used to estimate the prediction accuracy


Boechera stricta, a close relative of Arabidopsis. We identified nFT as the QTL altering the magnitude of phenological trait canalization, genetic constraint, and GxE. Both the magnitude and direction of nFT's canalization effects depend on the environment, and to our knowledge, this reversibility of canalization across environments has not been reported previously. nFT's effects on trait covariance structure (genetic constraint and GxE) likely result from the variable and reversible canalization effects across different traits and environments, which can be explained by the interaction among nFT, genomic backgrounds, and environmental stimuli. This view is supported by experiments demonstrating significant nFT by genomic background epistatic interactions affecting phenological traits and expression of the candidate gene, FT. In contrast to the well-known canalization gene Hsp90, the case of nFT may exemplify an alternative mechanism: Our results suggest that  genetic canalization, genetic constraint, and GxE may have related genetic mechanisms resulting from interactions among major QTL, genomic backgrounds, and environments.Natural populations exhibit substantial variation in quantitative traits. A quantitative trait is typically defined by its mean and variance, and to date most genetic mapping studies focus on loci altering trait means but not (co)variances. For single traits, the control of trait variance across genetic backgrounds is referred to as genetic canalization. With multiple traits, the genetic covariance among different traits in the same environment indicates the magnitude of potential genetic constraint, while genotype-by-environment interaction (GxE) concerns the same trait across different environments. While some have suggested that these three attributes of quantitative traits are different views of similar concepts, it is not yet clear, however, whether they have the same underlying genetic mechanism. Here, we detect quantitative trait loci (QTL) influencing the (co)variance of phenological traits in six distinct environments in  Biological traits often display large amounts of genetic variability as well as genetic correlations among traits. This variability provides the raw material for evolutionary change and may alter the direction of trait evolution under selection. Despite this importance, it is unclear whether the genetic controls of variability in single traits and relationships among multiple traits have related mechanisms. Using the flowering time of a plant species as model, here we performed genetic mapping and identified a locus altering single-trait variability and multi-trait relationships. The effect likely results from the distinct thresholds required by its different alleles to trigger flowering, which can be explained by the interaction among this major locus, the variable genomic backgrounds, and the distinct environments. This view is supported by experiments showing epistatic effects of this major locus on flowering time and expression pattern of the candidate gene. Together, our results show that, at least for traits with major signal integrator genes such as flowering time, the genetic control of single-trait variability and multi-trait relationships may have a common underlying mechanism that may be generalizable to other genes or pathways, mediated by interaction among major loci, genomic backgrounds, and surrounding environments. Arabidopsis thalianaElucidating the genetic basis of quantitative traits enables analysis of the processes that shape trait evolution PV, can be decomposed as PV = EV+GV+GxEV+eV, where EV is the major environmental variance from different growth chambers or experimental gardens, GV is the genetic variance, GxEV stands for the genotype-by-environment interaction, and eV is the stochastic noise caused by micro-environmental differences or other factors. For experiments across several different major environments, ‘plasticity’ consists of EV and GxEV. Within the same major environment (where EV and GxEV can be ignored) canalized traits exhibit little phenotypic variation (PV) environmental canalization reducing eV), or genetically distinct individuals produce similar phenotypes despite different genetic backgrounds  eV or similar measures) of inbred lines was often used as a quantitative trait in standard mapping algorithms et al.GV), Fraser and Schadt For a quantitative trait, the phenotypic variation, G matrix G matrix of different traits in the same environment indicates the magnitude of potential genetic constraints, whereas the G matrix of the same traits in different environments is algebraically related to the genotype-by-environment interaction component of plasticity  The relationship among traits is often expressed in the form of their genetic variance-covariance matrix, the Boechera stricta, an ecological model organism closely related to Arabidopsis nFT) exhibits trade-offs in flowering probability and fitness across different natural environments Because plants often synchronize their phenology with specific environmental conditions B. stricta parents from Colorado and Montana, we performed mapping for loci that affect the among-RIL genetic variance  of phenological traits (flowering time and plant size [number of leaves] at flowering) in six different growth chamber environments. We identified three quantitative trait loci (QTL) under the stringent genome-wide significance threshold 0.01  (BST031941 and Bst004238) only had canalization effects on flowering time in one environment  flowering time, and the Montana genotype at Bst004238 on linkage group 7 caused flowering time canalization.Using recombinant inbred lines (RIL) between tations) . The sigironment : the ColnFT, had widespread canalization effects in multiple environments. This QTL is syntenic with the region containing flowering time gene FT  in Arabidopsis thaliana and is a major QTL influencing Boechera stricta phenology, life history and fitness in a broad range of environments FT gene locates within this region. The canalization effect of nFT was environment-dependent: under the genome-wide significance threshold of 0.01, its effect was significant for flowering time in four environments  different growth chamber environments, 2) distinct genomic backgrounds among RILs created by segregating genotypes of other flowering genes, and 3) the different input-signal threshold needed for either FT genotype to trigger flowering . In these slightly flowering-inhibiting environments, most genomic backgrounds generated lower input signals, which were still enough for the low-threshold Montana genotype to express , whereas a portion of families with the Colorado genotype did not flower until the second growing season because many genomic backgrounds did not generate enough input signals for the high-threshold Colorado genotype . In these flowering-inhibiting environments where most genomic backgrounds generated low input signal, some genomic backgrounds still had enough signal for the Montana genotype to flower in the first season, but some families with Montana genotype flowered only in the second season  of G matrices in different trait-by-environment combinations: flowering time in six environments, leaf number at flowering in six environments, and the combination of all 12 traits  and between the same traits in different environments (indicating the magnitude of the genotype-by-environment interaction component of plasticity). Again, nFT and BST031941 were the only QTL influencing most trait pairs. Similar to the canalization result for univariate traits (above), nFT altered the genetic covariance structure between flowering time and leaf number only in both vernalization lengths of two ambient environments: 12 hour days, 18°C and 16 hour days, 25°C, but not 16 hour days, 18°C  between two G matrices in each case. BST031941, on the other hand, had effects only in environment 16 hour days, 25°C, 4 week vernalization and altered both the size and orientation of the G matrix  interactions  and the cumulative effect from upstream genes (the genomic background), and epistasis between nFT and individual upstream QTL may be too weak to detect in the previous experiment.Since ther QTL . These rnFT and genomic background, we conducted greenhouse experiments using several heterogeneous inbred families (HIF). Each family had almost identical genomic background and segregated for the two nFT genotypes, and the use of several such families allowed the test for genomic background by QTL epistatic effects (nFT by genomic background (HIF) interactions for all three traits in the greenhouse environment  and genomic background (P<0.001), as well as nFT by genomic background interaction effect (P = 0.005). nFT by genomic background reaction norms for each pair of traits, demonstrating this epistatic effect.In multivariate analysis (MANOVA) simultaneously treating all three traits as response variables, there were significant main effects for FT gene, the HIF phenotypic experiments only showed effects of the nFT QTL. To further test this prediction that the FT gene interacts epistatically with other flowering genes in the genome, we used the same HIF experimental design (nFT by HIF (genomic background) interaction effect on expression of the FT transcript, using two HIF backgrounds. This interaction effect was highly significant  and quantitative expression of the FT transcript in individual plants . This supports that complex trait variation at the nFT QTL may be functionally mediated by the FT locus itself.While our ‘threshold hypothesis’ focused on the effect of the l design  to test nificant . While tnificant . In HIF genotype . This obB. stricta by showing how one QTL  influences all three attributes for phenological traits of Boechera stricta. nFT influences single-trait genetic canalization, and the magnitude and direction of its effects can be reversed across environments. nFT's environmentally dependent and reversible effect in one trait, when extending to multiple traits, creates the distinct patterns of covariance structure among different traits in the same environment  or among the same traits in different environments . We propose a ‘threshold hypothesis’  experiment, echoing studies showing the prevalence of epistasis in both trait and molecular evolution The genetic basis and evolutionary history of canalization in one trait, genetic constraint among multiple traits, and genotype-by-environment interaction (GxE) across different environments are active foci for research in evolutionary genetics sis’ see  to explanFT on flowering time, and the concept is illustrated in FT, the genomic backgrounds with different combinations of polymorphic upstream genes , and multiple growth chamber environments that also generate different levels of input signals. In this hypothesis, the activation of FT expression (which then triggers flowering) depends on whether the upstream input signals, which vary with different combinations of genomic backgrounds and environmental stimuli, exceed the genotype-specific threshold of FT. The interaction among major threshold gene, genomic backgrounds, and environmental stimuli therefore triggers the environment-dependent canalization effect of flowering. The threshold model may also help explain how discrete and large-effect phenotypic changes may be caused by continuous and small-effect upstream genetic mechanisms.In this study we proposed a ‘threshold hypothesis’ to explain the environment-dependent genetic canalization effects of FT expression is binary: input signals generated by different backgrounds or environments are either below or above the threshold for FT alleles to express. In a previous study of Arabidopsis thaliana, Welch et al.et al.FT alleles with different thresholds simply have different response curves  FT gene is trigged by signals from upstream genes. As a consequence, we predict that distinct input-signal requirements for FT's different genotypes may generate QTL by genomic background interaction effects on phenological traits and on its own expression pattern, which is supported by our HIF experiments. Therefore, in contrast to Hsp90, whose specific function may not easily be extrapolated to most genes or pathways, our threshold hypothesis and the case of the FT gene in the flowering time pathway may represent an alternative mechanism for other cases of canalization, genetic constraint, and genotype-by-environment interaction in traits with major signal integrators such as flowering time.Our threshold hypothesis also echoes the recent idea that cryptic genetic variation (CVG) is not ‘mechanistically special and mysterious’ Hsp90. Further studies supported this model by showing that gene knock-outs can affect both genetic and environmental canalization of yeast gene expression FT gene in this study. While these previous studies focus on artificial gene knockouts, here we provide an example of trait canalization from natural variation for ecologically important traits.In fact, a similar idea has been proposed and tested previously FT, the current focus of the threshold hypothesis, and therefore it is more straightforward to classify environments based on their effect on flowering promotion  instead of by specific environmental factors . For flowering time, pathways responding to different environmental signals converge at floral signal integrator genes such as Arabidopsis thaliana. Stinchcombe et al.FRIGIDA but not for the deletion allele (ΔFRI), and the flowering time of accessions bearing the deletion allele is canalized. This canalization effect is caused by epistasis between FRIGIDA and FLCΔFRI allele suppressed the effect between different alleles of FLC. Similarly, in our study we identified nFT as the canalization locus and demonstrated the epistatic effects in the HIF experiment, where the different nFT genotypes alter the phenotypic effect of different genomic backgrounds . In addition, as in other cases of canalization genes nFT's canalization effect depends on the environment.The link between epistasis and genetic canalization of flowering time has been established in the model plant Drosophila have shown that traits with higher fitness effects have greater canalization et al.Hsp90 gene in Drosophila may be favored because it buffers against potentially unfit background genetic variation. On the other hand, the non-canalizing allele might be favored when a trait is under directional or disruptive selection. Under both scenarios, however, the allelic polymorphism in canalization genes will be eliminated if trait canalization is universally favored or disfavored by natural selection. Our results provide a mechanism where the polymorphism of canalization genes can be maintained. Because which nFT genotype has the canalization effect depends on specific environments, different genotypes may be favored under distinct environments even with consistent natural selection for or against trait canalization, beyond mutation-selection balance The adaptive value of canalization has received considerable attention nFT canalization may also maintain the molecular polymorphism of other flowering genes in the genome. Canalization may change the selective influence on other genes by suppressing the genetic variation expressed in traits heat shock protein 90 (Hsp90), the wild type allele buffers the phenotypic effect of potentially deleterious mutations in the genome, thereby reducing the force of purifying selection on these mutations Boechera stricta flowering time, however, may be more complex due to the nFT by environment interaction effect on canalization. Even if the selection force on flowering time is identical across populations, other flowering loci in the genome may still be subject to different types and magnitude of natural selection depending on local environment and nFT genotype. Such variation in selection may in turn influence the molecular polymorphism of other flowering time genes.The environmental dependence of nFT locus also influenced the (co)variance of ‘leaf number when flowering’, a well-defined quantitative trait often used as an indicator of the reproductive phenology. We therefore think these phenological traits reflect important underlying biological processes.In this study, flowering time was defined as the days elapsed since initial vernalization, excluding the duration of the second vernalization for plants that did not flower in the first growing season. Since the time of vernalization simulated ‘winter’ conditions with little plant growth, this approach quantifies the number of growing-season days the plants experienced before first flowering. Our results and the threshold hypothesis suggest that the canalization effect primarily reflects whether plants flowered in the first growing season, and therefore this approach captures both the variance between and within seasons. In addition to flowering time, the G matrix) indicates the magnitude of potential genetic constraints and can have profound effect on the magnitude and direction of trait evolution under selection G matrix evolution among evolutionary lineages G matrix difference. In Arabidopsis, Stinchcombe et al.ERECTA gene confer different structure of the G matrix among four traits. In mice, Wolf et al.The covariance structure among multiple traits  between different traits in the same environment (indicating the magnitude of genetic constraint), and 2) the same trait between different environments . This supports the idea that genetic constraint and plasticity are related concepts nFT Colorado genotypes canalize flowering time, but there is no nFT canalization effect for leaf number , one genotype of the QTL may exhibit similar phenotypes across diverse environments while the other genotype has varying phenotypes. While we did not specifically map for this macro-environmental canalization, the genetic mechanism altering EV may also be realized from the threshold hypothesis  nFT's role as an epistatic modifier of other flowering genes and 2) the effect of other flowering genes (different HIF genomic background) on gene expression of the FT locus itself, a network hub integrating signals from upstream genes in the flowering time pathway. These observations are consistent with the ‘threshold hypothesis’ illustrating how flowering pathway function can generate epistasis between FT and other flowering genes (ArabidopsisArabidopsis flowering genes FRIGIDA (FRI) and FLOWERING LOCUS C (FLC) FT responds to the combined effect of multiple upstream pathways, and the one-to-one epistasis between nFT and individual flowering time loci may be too weak to be detected by our previous B. stricta, this epistatic relationship between nFT and genomic background has been supported by our HIF experiment.Results from the HIF experiment show strong ng genes  and alsonFT. Although it might be possible that the nFT QTL's effect on trait mean, variance, and covariance structure are effects of several closely linked genes, our threshold hypothesis and following HIF experiments both suggest that the FT gene may exhibit these pleiotropic effects: being a floral signal integrator, the two FT alleles may influence trait means due to different thresholds for activation by upstream signals . Such threshold differences may interact with various genomic backgrounds or environmental stimuli and thus alter the pattern of trait (co)variation (see In this study we employed a linkage mapping approach to map (co)variance QTL, and the issue of sample size and statistical power may be a limitation tion see . FurtherAll RIL data were obtained from our previous study N = 5 individuals/RIL/treatment and N = 35 individuals/parental line/treatment) in six distinct environments, composed of two vernalization lengths (four or six weeks) at 4°C and three growth conditions . In this study, we analyze family mean trait values for the 178 RIL and 2 parental lines obtained from the previous study In the previous study, we measured flowering time and leaf number at flowering  using scripts available upon request from CL.For each genetic marker, we used the Brown-Forsythe test, a modification of Levene's test based on median, to estimate the difference in trait variance between the Colorado homozygote and the Montana homozygote at markers across the genome. This approach is similar to Shen et al. pV) can be decomposed into:mV is the variation explained by the difference in mean of the two homozygous genotypes, vV is the variation explained by the difference in variance of the two genotypes, and rV is residual variance arising from other sources mV and vV, following previously published equations designed for populations with two homozygous genotypes in each SNP p and q are the genotype frequencies of the Colorado and Montana homozygotes, respectively. COμ and MTμ are the mean, and COσ and MTσ represent the standard deviation of the Colorado and Montana homozygotes.Considering the effect of a QTL, the total trait variation (G matrix with 12 traits); 2) flowering time in all environments (G matrix of six traits); 3) plant leaf number at flowering in all environments (G matrix with six traits). We further mapped QTL changing the covariance structure between flowering time and plant size at flowering separately for each environment (representing the magnitude of genetic constraint) and between the same trait in pairs of different environments . Among the multiple ways to model plasticity  flowering time and plant size at flowering (number of leaves) in all six environments (G matrices) were estimated, and we assessed the QTL effect by comparing the G matrices via three methods: 1) Box's M statistics; 2) the angle between Gmax; 3) the Krzanowski index. Statistical significance is determined by the genome-wide permutation algorithm described above. We acknowledge that the covariance matrix estimated from family means may not be identical to the genetic covariance matrix estimated from individual-level mixed-model MANOVA. This simplification, however, was necessary to ensure computational feasibility since the G matrices needed to be calculated twice (one for each homozygous genotype of a marker) for ∼160 markers for each of the 1,000 permuted data sets.For each molecular marker, we separated the data into two groups of homozygous genotypes. Two separate (co)variance matrices (g is the number of matrices to be compared (two in our case), iV is the degrees of freedom, and iS is the trace of the i-th matrix. N, the overall degrees of freedom, is the sum of all iV values. The trace, S, of the pooled covariance matrix is:G matrices from the two genotypes at each genetic marker. Traditionally the significance is determined by an F-test and is sensitive to deviations from multivariate normality, but our genome-wide permutation procedure alleviates this parametric distributional requirement.Box's M statistic G matrices max , we first calculated the angle between the first eigenvector, u and v, of the two G matrices respectively:θ may be larger than π/2 . Therefore if θ is larger than π/2, the radian angle between Gmax is calculated as π - θ, otherwise the angle equals θ. This method estimates the angular difference between the respective axes with most variation in each G matrix.Two covariance matrices could differ not only in size but also in their orientation. We used two methods to compare the orientation between max method, however, has a caveat that when G matrices have many dimensions (traits), other principal components may carry substantial amounts of variation, and comparing Gmax may not be sufficient k-dimensional subspace between two G matrices, where k is less than or equal to half of the dimension of the original G matrix. For example, in a data set with 10 traits, we estimated the degree of similarity between two subspaces formed by the first five eigenvectors of two G matrices. Similar to the Gmax method above, each eigenvector w that will be used in the analysis was first standardized by the square root of its dot product:S) then is calculated as:A and B are matrices containing the first five standardized eigenvectors of the two respective G matrices, and superscript T denotes matrix transpose. As in other studies S matrix (the Krzanowski index) as a measure of overall similarity between the two subspaces. This index ranges from 0 to 5 in our example of 10 traits, with 0 signifying non-overlap and 5 indicating total overlap between subspaces. For our purpose of mapping QTL whose different genotypes confer the most dissimilar G matrices, we compared the negative Krzanowski index of each marker to the 1,000 maximum negative Krzanowski indexes from permutation.The Gmax and Krzanowski methods compare the orientation of linear relationship among traits, Box's M tests the dispersion of points from this linear relationship. All mapping algorithms were written in R (http://www.r-project.org/). When only two traits are involved, the angle between Gmax captures all the difference in orientation between G matrices, and therefore the Krzanowski method is not necessary.In summary, while the GnFT and other flowering time QTL identified in the same growth chambers from our previous study nFT, the other QTL, and their interaction as fixed-effect predictor variables in each model.To test the existence of epistasis as predicted by the threshold hypothesis, we performed analysis of variance for the interaction effect between nFT and mostly homozygous at other markers. From each F5 parent we planted approximately 250 seeds, which are self-full siblings of the original genotyped F6 individual in Anderson et al.N = 1097 plants total from four F5 parents). We genotyped the microsatellite marker C02 nFT homozygous genotypes. With four HIFs that are different in genomic background, the interaction between nFT genotype and HIF (genomic background) provides a statistical test for epistatic effects on phenology.We generated four heterogeneous inbred families HIFs,  to test nFT genotype, we selected at least 20 homozygous families from each HIF , for a total of 89 families. In November 2011 we place 10–15 seeds from each of the 89 families on moist filter paper in petri dishes in dark conditions at ambient temperature for 3 weeks until germination. As in other B. stricta greenhouse experiments The HIF experiment was conducted in the Duke University Greenhouse rather than in multiple growth chamber environments as in the RIL experiment. To provide independent replication for each homozygous N = 785 F7 individuals flowered successfully). No individuals flowered after that date. Relevant data are available in In January 2012, all rosettes were vernalized at 4°C for 8 weeks. Plants were removed from vernalization on 29 February 2012, at which point we monitored them 7 days/week and recorded the date of first flowering as well as the number of leaves and plant height at first flowering. By April 23, 2012, we had collected phenological data from 8–10 full siblings per family (nFT genotype (Montana/Colorado homozygote), and nFT by HIF interaction . We incorporated ‘family’  and block as random effects. We then conducted univariate ANOVA for each response variable with the same statistical model.Statistical analysis was performed with REML mixed-model ANOVA . We first conducted a multivariate ANOVA (MANOVA) to address how the three response variables  varied with HIF (3A/89A/98A/105A), nFT locus in different environments suggests a three way interaction of the major QTL (nFT) by genomic background (the combination of other flowering-related genes) by environment conditions, and the interaction between nFT and genomic background on phenological traits is tested in the HIF experiment. The nFT locus contains the ortholog of the FT gene in Arabidopsis (AT1G65480). FT serves as a major hub for integrating upstream signals of flowering, and its expression often correlates with the onset of flowering FT gene in Boechera stricta is responsible for the differential canalization effect of the nFT QTL in our Montana by Colorado cross, its expression pattern should vary depending on the nFT genotype and genomic background. We therefore test the expression pattern of FT in the same HIF experimental design.The contrasting canalization effect of the nFT genotype for a total of 20 families. Forty experimental plants  were completely randomized, and all planting procedures and greenhouse environmental settings were as above. Rosettes were grown in the Duke greenhouse for 12 weeks and stratified at 4°C for 8 weeks. In Arabidopsis, FT mainly expresses in leaves, where protein translation happens, and the proteins are transferred to floral meristems FT in Arabidopsis exhibits circadian rhythm in gene expression, and under 16-hour days, its maximum expression is in the end of daytime Two HIFs (HIF 89A and HIF 98A) were used in this experiment. Within each HIF we obtained five families from each homozygous FT gene copy in Boechera stricta . Therefore, we cloned and sequenced FT full-length coding sequences from both parents. Only one copy is expressed, and both parents have the same expressing copy with identical coding region sequences . All primer sequences are available in FT gene expression was measured by quantitative PCR (qPCR) with Thermo Scientific DyNAmo SYBR Green qPCR Kits. Following previous experiments ACTIN2 gene (ACT2) is used as reference gene, and FT expression level for each of the 38 samples was calculated as:ACT2Ct is the Ct value in qPCR of the reference gene ACTIN2, and FTCt is the Ct value of FT. Since within each sample the Ct value of FT is always larger  than ACT2, ΔCt is always negative, and larger ΔCt represents higher FT gene expression. The relative qPCR signal of FT to ACT2 can be calculated as 2CtΔ. This 2CtΔ value, however, has a skewed distribution among samples. Since log transformation of 2CtΔ yields a value that is proportional to ΔCt, we used the original ΔCt as the response variable for statistical analysis. Relevant data are available in Our partial genomic sequencing shows that there may be more than one nFT genotype, HIF, and nFT by HIF interaction were treated as fixed effects, and family was treated as a random effect nested within nFT and HIF. All 40 plants were grown in the same block, so no block effect exists for this experiment. To further test if FT expression in Boechera stricta is related with flowering, we recorded whether each of the 40 experimental plants had visible flowering buds during the time of leaf-tissue collection. The analysis incorporates ΔCt as the response variable, and the phenological indicator ‘whether a plant has visible bud’ as a fixed-effect categorical predictor, and family as random-effect predictor variable.Statistical analysis was performed as in the HIF phenotypic experiment, where Figure S1QTL controlling the variance of phenological traits in growth chamber environments. Each row represents a trait in one environment. The six upper rows are flowering time, and the six lower rows are leaf number when flowering in six different environments. Texts beside each row represent the environment and trait. For example, ‘12 H, 18 C, 4 W, FT’ refers to flowering time under 12 hour days, 18 degree C, and 4 weeks of vernalization, and ‘16 H, 25 C, 6W, LN’ refers to leaf number under 16 hour days, 25 degree C, and 6 weeks of vernalization. Each column represents a genetic marker on the linkage map, and chromosomes are separated by vertical white lines. Black cells represent markers significantly controlling the variance of a trait, whereas dark grey cells are non-significant markers. Light grey cells are markers that are excluded due to segregation distortion (see main text).(PDF)Click here for additional data file.Figure S2P< = 0.05, ** P< = 0.01, *** P< = 0.001.Flowering time distributions of families with the Montana (red bars) or Colorado (blue bars) homozygous genotypes of two QTL (BST031941 and Bst004238) in the environment with 16 hour days, 25°C, and 4 weeks of vernalization. Above each graph, horizontal bars denote the mean plus or minus one standard deviation for each allele, numbers on the left denote percent of total variation explained by the difference in variance of the two alleles, and asterisks on the right denote genome-wide significance of the difference in variance. * (PDF)Click here for additional data file.Figure S3nFT locus in six environments. Panels in a column have the same ambient environment: first column – 12 hour days 18°C, second column – 16 hour days 18°C, third column – 16 hour days 25°C. Panels in a row have the same vernalization treatment: first row – 4 week vernalization, second row – 6 week vernalization. Vertical dashed lines (180 days) separate the two growing seasons in each environment. Above each graph, horizontal bars denote the mean plus or minus one standard deviation for each allele, numbers on the left denote percent of total variation explained by the difference in variance of the two alleles, and asterisks on the right denote genome-wide significance of the difference in variance. * P< = 0.05, ** P< = 0.01, *** P< = 0.001.‘Leaf number when flowering’ distributions of families with the Montana (red bars) or Colorado (blue bars) homozygous genotypes of (PDF)Click here for additional data file.Figure S4QTL controlling the covariance structure of phenological traits in growth chamber environments. Each row represents a statistical method on a group of traits across several environments. For example, ‘Box's M, all traits’ represents the results of Box's M method on flowering time and leaf number from all six environments , and ‘Krzanowski, leaf number’ represents results of Krzanowski method on leaf number in six environments. Each column represents a genetic marker on the linkage map, and chromosomes are separated by vertical white lines. Black cells represent markers significantly controlling the covariance of a group of traits, whereas dark grey cells are non-significant markers. Light grey cells are markers that are excluded due to segregation distortion (see main text).(PDF)Click here for additional data file.Figure S5The effect of QTL BST031941 on the structure of covariance matrix among standardized flowering time in all environments. Each dot represents the trait value of one recombinant inbred family, and an ellipse represents the 95% confidence region of the covariance matrix defined by an allele. Montana allele: black dots and solid ellipse. Colorado allele: white dots and dashed ellipse.(PDF)Click here for additional data file.Figure S6max angle method (ellipse orientation). Montana allele: red dots and ellipse. Colorado allele: blue dots and ellipse. ** P< = 0.01, *** P< = 0.001.The effect of QTL BST031941 on the structure of covariance matrix between standardized flowering time and leaf number when flowering in each of the six environments. Asterisks on the upper right of each graph denote genome-wide significance for the Box's M method (ellipse size), and asterisks on the upper left of each graph denote significance for the G(PDF)Click here for additional data file.Figure S7max angle method (ellipse orientation). * P< = 0.05, ** P< = 0.01, *** P< = 0.001.The effect of QTL BST031941 on the plasticity of standardized phenological traits. Each graph shows the relationship of the same trait  between pairs of environments. Montana allele: red dots and ellipse. Colorado allele: blue dots and ellipse. In each graph, asterisks in the upper right denote genome-wide significance for the Box's M method (ellipse size), and asterisks on the upper left denote genome-wide significance for the G(PDF)Click here for additional data file.Figure S8nFT locus. Shown are examples of two HIF. Each HIF was generated from one F5 parent that is almost homozygous across the genome but heterozygous for the nFT locus. The F5 plant is self-fertilized to generate many F6 plants, and all of them are genotyped for nFT. The F6 plants that are homozygous for nFT are self-fertilized to generate F7 plants for the experiments. All F7 siblings from the same F6 parent are nearly clones to each other, and all F7 plants within a HIF are almost identical in the genome but segregating for two homozygous nFT genotypes. Different HIF differ in genomic background, therefore allowing the test for nFT by genomic background interaction effect.Generation of Heterogeneous Inbred Family (HIF) for the (PDF)Click here for additional data file.Figure S9y = 1/(1+exp(a * (−x+b))), x is the upstream input signal from different genomic backgrounds or environments , a determines the width of the log phase in the sigmoid curve, and b determines the x coordinates where the log phase is centered. The sigmoid model approximates the threshold hypothesis when the value of parameter a becomes larger, which makes the log phase narrower and finally converge at coordinate b, the threshold. The sigmoid function of the Colorado (panel A) and the Montana (panel B) genotypes of FT simply differ in their threshold, the value of parameter b and b′ as marked by the vertical dashed blue and red lines. Panel C is similar to The threshold hypothesis is related with the sigmoid model of gene regulation. In a sigmoid model (PDF)Click here for additional data file.Table S1P values  between 12 phenological traits in this study.Pairwise genetic correlations  and the (DOCX)Click here for additional data file.Table S2Trait loadings on the first two principal components for all traits, flowering time traits, and leaf number traits shown in (DOCX)Click here for additional data file.Table S3nFT and other flowering-time QTL identified in a previous study.Statistical tests of the interaction effect (epistasis) between (DOCX)Click here for additional data file.Table S4Primer sequences used in this study.(DOCX)Click here for additional data file.Dataset S1nFT by HIF effect on phenological traits. Block: Experimental blocks, as categorical random effect; Flowering_time: Days of first flowering after vernalization, as numeric response variable; Leaf_number_at_flowering: Leaf number when flowering, as numeric response variable; Height_at_flowering: Plant height at flowering (cm), as numeric response variable; nFT_genotype: The genotype at the C02 microsatellite locus near nFT QTL, as categorical fixed effect; HIF: HIF family, as categorical fixed effect; Family: The F6 individuals those experimental F7 plants were descended from, as categorical random effect nested within HIF and nFT_genotype.Data for the greenhouse experiment for (TXT)Click here for additional data file.Dataset S2nFT by HIF effect on FT gene expression. Plant_ID: ID of individual plants; HIF: HIF family, as categorical fixed effect; Family: The F6 individuals those experimental F7 plants were descended from, as categorical random effect nested within HIF and nFT_genotype; nFT_genotype: The genotype at the C02 microsatellite locus near nFT QTL, as categorical fixed effect; Visible_bud: Whether the individual plant has visible flowering buds at the time of tissue collection; delta_Ct: Ct value of ACT2 minus FT.Data for the greenhouse experiment for (TXT)Click here for additional data file.