Foxtail millet [Setaria italica (L.) P. Beauv.] is one of the oldest cereals in the Old World. It is characterized by diploidy with small chromosome numbers (2n = 2x = 18), small genome size (approximately 500 Mb), an inbreeding habit, and a relatively short growth habit; therefore, it has become an ideal model plant for genetic studies on panicoid grass species, including switchgrass and Napier grass, which are considered as biofuel sources, and other cultivated millet species such as pearl millet1. This millet adapts to various environmental conditions, and its agronomic traits show large variation as a result of adaptation to local environments ranging from temperate to tropical climates, high- and low-altitude conditions, and cultivation under various cultural conditions. Several landrace groups are genetically differentiated and distributed in different geographical areas2. The foxtail millet genome has been sequenced3,4 and recently, the genome of its presumed wild ancestor, S. viridis, was also determined5. Owing to its high variations in several agronomic traits, this millet will also be a good material for studying crop evolution in the context of adaptation to variable environmental conditions and human selection.

Recently, next-generation sequencing (NGS) technology has become a powerful tool for genetic mapping and population genetics. Several methods for genetic mapping using NGS have also been developed, including genotyping by sequencing (GBS) 6,7, RAD-seq8,9, ddRAD-seq10,11, QTL-seq12, and GRAS-Di13,14.

Several studies on gene and QTL mapping15,16,17,18,19,20,21,22,23 and genome-wide association studies (GWAS)24,25,26 in foxtail millet have been conducted using NGS technology, and several genes have been mapped and identified successfully. However, most studies on QTL mapping have been carried out using hybrid-derived populations from crosses within Chinese cultivars, Japanese cultivars, and between Setaria viridis and a Chinese cultivar. No population between distantly related landraces collected from different geographical conditions has been used for mapping.

Consequently, we constructed an RIL population derived from a cross between a Japanese landrace (JP71640) and a Taiwanese landrace (JP73913) adapting to different latitudes and climates and mapped three traits: leaf sheath color, spikelet-tipped bristles (stb), and days to heading (DTH) (Fig. 1). JP 71640 and JP 73913 were chosen as parents because they are genetically distinct from each other in terms of morphological and physiological characteristics, rDNA genotypes, RFLP variations of genomic DNA, and intervarietal hybrid sterility2. Herein, we successfully identified major QTLs and identified candidate genes for the C gene controlling leaf sheath color, a homeobox (HOX14) gene for stb, and PRR37 for DTH. We also found allelic variation in the C gene and the homeobox gene in Yugu1 and naturally occurring mutants of S. viridis, respectively. The geographical distribution of the TE-insertion type of S. italica PRR37 (SiPRR37) will be discussed in terms of its adaptive significance.

Figure 1
figure 1

Characteristics of parental landraces. Maternal parent: JP73913 from Taiwan with green leaf sheath and spikelet-tipped bristles (stb) and heading early-middle August. Pollen donor: JP71640 from Miyazaki Prefecture, Japan, with red leaf sheath and wild type of bristles and heading early September. The map was created using the R package “maps” ver. 3.3.0 (


Segregation of traits

Stb and the green leaf sheath are recessive traits27, as we previously reported in the F2 population. Two types of leaf sheath colors, red and green, were observed in 49 and 41 lines of the RILs, respectively. This result fits the 1:1 ratio using the Chi-square test (P > 0.05). Common wild-type bristles and mutant stb (Supplementary Fig. S1) are observed in lines 43 and 47, respectively. This result also fits the 1:1 by Chi-square test (P > 0.05). Days to heading (DTH) showed a rather broad but bimodal distribution in all cultivations in 2018, 2019, and 2020, and a high positive correlation in DTH between different years was observed (Fig. 2).

Figure 2
figure 2

Histograms showing variation of DTH in foxtail millet RILs in 2018, 2019, and 2020 and correlation between different years. The diagonal from the upper left to the lower right : Histograms showing variation DTH in foxtail millet. Upper right: Correlation coefficients between different years. ***P < 0.001. Lower left: Scatter diagrams of DTH of RILs between different years.

Construction of high-density linkage maps

The genomes of all RILs for the F10 generation were subjected to flexible ddRAD-seq to detect genome-wide SNPs and Presence/Absence (PAs) markers, which were then used to construct a high-density linkage map. Following the quality-control steps, a total of 6,818 SNPs and 3,430 PAs were detected using ddRAD-seq. By adding 153 SSR/INDEL markers to these, 37 linkage groups corresponding to chromosomes I-IV3 were constructed (Fig. 3, Supplementary Table S1). As shown in previous research20,21,22, the S-shape correlation of markers between physical distances and genetic distances was observed (Supplementary Fig. S2).

Figure 3
figure 3

A high-density linkage map of the RILs of foxtail millet based on the flexible ddRAD-seq. Chromosome numbers correspond to S. italica reference genome, GCF_000263155.2, and the alphabets mean linkage group. The linkage group with red alphabets has been constructed using markers that the segregation distortion does not fit the expected ratio (1:1).

QTL mapping and identification of candidate gene

Leaf-sheath color

The QTL analysis detected a genomic region strongly associated with leaf sheath color in linkage group IVb, which corresponds to chromosome IV, as expected in a previous study27 (Fig. 4a, Supplementary Table S2). A candidate gene, C, which encodes the anthocyanin regulatory C1 protein (LOC101756616), was closely located with a marker showing the highest LOD score (Fig. 4b), as Jia et al.24 suggested. We compared the genome sequence between JP71640 with a red leaf sheath and JP73913 with a green leaf sheath. JP71640 has a complete C gene sequence, but JP73913 has a large insertion (ca. 6.5 kb) in exon 2 (Fig. 4c). It is inferred that this gene loses its function in the green leaf sheath. Interestingly, another accession, Otsuchi10 with red leaf sheath, had no insertion in this gene, but Yugu1 and Nisatai-zairai, with a green leaf sheath, had a large insertion (ca. 5.1 kb) in exon 3 (Fig. 4c). Homology search using Censor ( showed that a large insertion found in exon 2 is a Copia-type retrotransposon (Copia 6 Sit), and the other found in exon 3 is another Copia-type retrotransposon (Copia 20 Sit). It is strongly suggested that these transposable element (TE) insertions are causal mutations in the green leaf sheath.

Figure 4
figure 4

Analysis of leaf sheath color of the foxtail millet. (a) Distribution of LOD scores for the leaf sheath colors in RILs. (b) Enlarged view of the physical map around the marker which showed the highest LOD score. The annotated genes on the S. italica reference genome are shown at the bottom part, and the red one is C gene which is the candidate gene for leaf sheath color. (c) Structure of C gene for leaf sheath color. Transposable element (TE) insertions each for JP 73913 with green sheath and Yugu1 with green leaf sheath.


A genomic region associated with the stb phenotype was detected on chromosome II, as in our previous study27 (Fig. 5a, Supplementary Table S2). A homeobox-leucine zipper protein HOX14 (LOC101764951), which is a homolog of HvVrs1, and encodes a transcription factor responsible for the evolution of two-rowed barley to six-rowed barley28, was found 14 kb downstream of the SNP with the highest LOD score (Fig. 5b). Comparison of the genomic sequences of HOX14 between the parental accessions (JP73913 and JP71640) revealed an SNP at the 501st position of HOX14, causing an amino acid substitution from histidine to aspartic acid (Fig. 5c).

Figure 5
figure 5

Analysis of spikelet tipped bristles (stb) in foxtail millet. (a) Distribution of LOD scores for stb in RILs. (b) Enlarged view of the physical map around the marker which showed the highest LOD score. The annotated genes on the S. italica reference genome are shown at the bottom part, and the red one is HOX14 which is the candidate gene for stb. (c) Structure of HOX14 gene, a candidate gene for stb phenotype. A non-synonymous SNP presents in the exon 2. (d) Allelism test using cross between JP73913 and ‘Kyoto stb-1’ that is stb mutant of S. viridis. These two accessions and F1 hybrid between them showed stb phenotype. White bar indicates 10 mm. (e) Structure of HOX14 gene. Two SNPs specific to Kyoto stb-1 (S. viridis) are present in the exon 2 (middle table). The reference genome sequence of S. viridis, A10.15, was used as the wild-type (WT) sequence. The 444th SNP genotype in F3 individuals derived from a cross between Yugu1 and ‘Kyoto stb-1’ correspond to stb phenotype (bottom table).

To confirm that the causative gene was HOX14, we performed an allelism test using a naturally occurring stb mutant of S. viridis (Supplementary Fig. S3), which we discovered in Japan, and designated "Kyoto stb-1." It seems that this S. viridis mutant occurred independently of JP73913. We crossed it with JP73913 to successfully obtain F1 hybrids. The F1 individuals also showed an stb phenotype, suggesting that this S. viridis mutant is allelic to JP73913 in the stb causative gene (Fig. 5d). We sequenced the HOX14 gene of Yugu1 and Kyoto stb-1 and found two SNPs in the coding region, which altered the amino acid sequences of the protein, although these two SNPs were not present in wild-type S. viridis, A10.15 (Fig. 5e, DDBJ:LC642768). Furthermore, we investigated the co-segregation of the stb phenotype and genotype, which was genotyped using the KASP genotyping assay, at 444th position in the DNA binding domain of HOX14 in 92 F3 individuals derived from a cross between Yugu1 and ‘Kyoto stb-1’ (Supplementary Fig. S4). As shown in Fig. 5e, 38 individuals had the apparent stb phenotype with the AA genotype of the 444th SNP, and thirty-one individuals with the CC genotype of the SNP had the wild type of bristles. Twenty-three individuals had the wild type of bristles with the CA genotype (of the 23 individuals, 12 had only a few stbs on the tip of the panicle, probably because of heterozygosity (Supplementary Fig. S5), suggesting that this gene controls the trait.


Composite interval mapping (CIM) based on the data obtained from individual cultivations for the three years shown in Fig. 2 indicates that there is a QTL with a very high LOD score (Fig. 6a). Consequently, a QTL with a very high LOD score and a high percentage of phenotypic variation explained by QTL (PVE) values on chromosome II was commonly found for three years (Fig. 6a, Supplementary Table S2). One of the SNPs, NC_028451.1_49128686_A_C_0_2 marker, with a higher LOD score was located on a gene (LOC101758458) that showed homology to PRR37, which is involved in DTH in several grass species such as rice29, sorghum30, wheat31, and barley32. It has also been reported to be important in latitudinal adaptation (Fig. 6b). To clarify the association between DTH and the NC_028451.1_49128686_A_C_0_2 marker, the distribution of DTH values for genotypes of RILs at this marker is shown in Fig. 6c. The DTH comparisons between the JP73913 and JP71640 genotypes demonstrated an association between DTH and genotype every year. The JP73913 genotype for this marker accelerated heading, while the JP71640 genotype delayed it, with a difference of about 20 days between them (Fig. 6c).

Figure 6
figure 6

Analysis of days to heading (DTH) in foxtail millet. (a) Distribution of LOD scores for RILs in three years. PVE indicates the phenotypic variation explained by QTL. (b) Enlarged view of the physical map around the QTL. The annotated genes on the S. italica reference genome are shown at the bottom part, and the red one is SiPRR37 which is the candidate gene for DTH. (c) Box and dot plots of DTH between the different genotypes (JP73913 homozygous allele and JP71640 homozygous allele) at the marker on SiPRR37. P-values obtained by the student's two-sample t-test function in R are shown in each panel to assess statistical significance between the two genotypes of the RILs.

Geographical distribution of the TE-insertion-type SiPRR37 gene

Comparison of the genomic sequences of SiPRR37 between the parental accessions (JP73913 and JP71640) revealed a TE-insertion in the SiPRR37 intron of JP73913 (Fig. 7a). Yugu1, a variety of reference sequences for foxtail millet, also had a TE insertion in the same way. Recently, Li et al.26 also found that this gene, SiPRR37, is key to adaptation in northeast China by GWAS, and they also reported TE-insertion in this gene. The TE found in this study and Li et al.26 are the same sequence and inserted in the same position in the gene, whereas they referred to the TE found in their study as Tc1–Marine. We also investigated the geographical distribution of the TE-insertion type of this gene in 99 accessions, as shown in Fig. 7b. Among the 99 accessions investigated, 55 were of the TE-insertion type, whereas 44 were not (Supplementary Table S3). The TE-insertion type is mostly distributed in tropical and subtropical regions and parts of East Asia. Contrarily, the non-insertion type is widely distributed in temperate zones. This insertion type was distributed in six of 12 accessions from China, and intensively in the Nansei-Islands of Japan, Taiwan, and Southeast Asia, including the Philippines, Indonesia, Thailand, and Myanmar; South Asia such as Nepal, India, and Pakistan; four accessions of Afghanistan; one accession of Ukraine; and one from Kenya. Two Japanese accessions from the northeastern part of Japan (Iwate Prefecture) also had this TE insertion. Specifically, the non-insertion-type SiPRR37 gene is mainly distributed in Japan, Korea, China, Central Asia, and Europe. Further analysis of this gene to heading will be required to understand adaptation of this millet to the latidude.

Figure 7
figure 7

The variant of SiPRR37 with TE-insertion and its geographical distribution. (a) Structure of the SiPRR37 gene and insertion of transposable element (TE). Primers used for the analysis of TE-insertion were shown as arrows. (b) Geographical distribution of TE-insertion type and non-insertion type (Wild type) of SiPRR37 gene of foxtail millet. The number next to the symbol indicates the number of accessions checked in this study. The map was created using the R package “maps” ver. 3.3.0 ( The X-axis and the Y-axis indicate longitude and latitude, respectively.

We found no TE-insertion of the SiPRR37 gene for all six accessions of S. viridis analyzed in this study.


We constructed RILs between JP 71640 and JP 73913, a Japanese and Taiwanese landrace of foxtail millets, which are phylogenetically and genetically distinct2. Various combinations of the characters between the parents were observed in cultivation experiments (data not shown), and the RILs constructed should be novel useful tools for crop evolutionary studies and breeding new varieties.

The flexible ddRAD-seq method employed in this study was highly effective for constructing a fine linkage map. We efficiently obtained more than 10,000 markers in this linkage map using flexible ddRAD-seq, whereas we obtained only 138 DNA markers, including SSR and transposable display (TD) markers27 in the F2 population between the same cross combination. This RIL population genotyped by flexible ddRAD-seq rapidly identified the candidate genes involved in this study’s morphological and agronomical traits. This population with a high density map will be useful for further mapping studies of other traits which were not investigated in the present study. In the present study, we used the MinION sequencer (Oxford Nanopore Technologies), in addition to the HiSeq X platform (Illumina). The de novo assembly using a combination of these platforms was also very practical for identifying the insertion of transposable elements into the gene.

We identified the candidate gene C gene, an MYB transcriptional factor for leaf sheath color, as suggested by Jia et al.24. Homologs of this gene have been reported to be involved in the pigmentation of many cereal plants such as rice, wheat, barley, and maize33,34,35. JP73913, a maternal parent of the RILs, has a Copia TE inserted in exon 2 of the gene, apparently causing loss of function of the gene. For Yugu1, a reference genome sequence of foxtail millet3 with a green leaf sheath, another copy TE was inserted in exon 3 of the gene, causing loss of gene function. These mutations caused by different TE insertions onto the same gene, which changed the red leaf sheath to green, should have occurred independently. Multiple origins of loss-of-function genes have been reported in waxy36,37 and polyphenol oxidase38 in foxtail millet. The green leaf sheath is also a good example of the multiple origins of the loss-of-function phenotype in foxtail millet. We are now investigating the origin of the green leaf sheath using more landraces from various Eurasian regions. The details will be published elsewhere because the origin of the green sheath seems more complicated.

Developing bristles in the genus Setaria, including foxtail millet, is important in the evolution of the bristle clade in the family Poaceae27. Stb1 mapped on chromosome II, as reported in our previous study27 and is located close to a homeobox (HOX14) gene, LOC101764951, a homolog of HvVrs1, the gene responsible for the evolution of two-rowed barley to six-rowed barley28. As HvVrs1 is a transcription factor involved in the development (suppression) of lateral spikelets in two-rowed barley, it is more likely that this homeobox gene suppresses the development of spikelets from the bristles and is functionally similar to the HvVrs1 gene.

We found that JP73913 with stb had a non-synonymous SNP in this gene but not in the homeobox domain. It is also possible that some SNPs and indels in the 5’ region upstream of the coding sequences may alter the gene expression pattern. We confirmed that a naturally occurring mutant ‘Kyoto stb-1’ gene is allelic to that of JP73913. We sequenced the coding sequence of the homeobox gene ‘Kyoto stb-1 and found two SNPs in the coding sequences (Fig. 5e). We confirmed stb and SNP in F3 individuals derived from Yugu1 and ‘Kyoto stb-1’ (Fig. 5e). Knockout of this gene by genome editing will be useful to confirm that this gene is responsible for stb.

For DTH, a QTL with a large effect was consistently found in the same region on chromosome II in all three-year trials. The SiPRR37 gene is located at the SNP with the highest LOD score (LOD value: 2018; 44.5, 2019; 30.2, 2020; 26.0). Interestingly, JP73913 has a Harbinger TE insertion in intron 3, whereas JP71640 does not. Yugu 1 also had a TE insertion in this intron. Takei and Sakamoto39,40 reported that variation in the heading date of foxtail millet is determined by the length of basic vegetative growth and sensitivity to daylength. Mauro-Herrera et al.15, and Yoshitsu et al.23 investigated QTLs on DTH in foxtail millet and found some QTLs such as qDTH2 and qDTH7 but did not suggest the SiPRR37 gene in their mapping populations. Recently, Li et al.26 reported that SiPRR37 plays an important role in the adaptation of Chinese cultivars to high latitudinal regions in China. In this study, we also found a large LOD peak of QTL on chromosome II in our population and found that SiPRR37 is a candidate gene for the difference in DTH between the parents. A TE was inserted in this gene of JP73913, which is the same as that reported by Li et al.26. The analyses of 99 accessions covering the whole traditional distribution area of foxtail millet landraces revealed that TE-insertion type is mainly distributed in parts of Japan and China and subtropical and tropical regions of Eurasia, such as Taiwan, Southeast Asia, and South Asia. Ranges of DTH of landraces showing non-TE-insertion type (34–116 days) and that of landraces with TE-insertion types of SiPRR37 gene (42–169 days ) overlapped in our data obtained in cultivation experiment in Shobara, Hiroshima, in 201142 (Supplementary Table S3) but TE-insertion type is mainly distributed in the middle latitudal region. In the middle latitudinal region, photosensitivity to daylength is important in the adaptation of landraces, whereas high-latitude and low-latitude region sensitivity to daylength are not always necessary39,40. TE-insertion into the SiPRR37 gene leading to loss or reduction of function of the gene is essential for the spread of foxtail millet in low-latitude areas such as the tropical and subtropical regions, as found in this study and high latitudinal areas in China, as reported by Li et al.26. SiPRR37 plays important role in adapting to latitudinal areas in other cereals, such as rice29 and sorghum30. This work strongly suggests that insertion of the TE in SiPRR37 is key to elucidating adaptation to not only high latitude but also low latitudinal areas in Asia. Interestingly, six accessions of green foxtail, S. viridis, did not have this insertion in the gene, although the number of accessions is still limited. Insertion of the TE in the SiPRR37 gene might have occurred after domestication. Further analysis of more accessions of green foxtail and foxtail millet will reveal the spread of TE-insertion type in Eurasia.

The naturally occurring splicing variant Heading date1 (HD1) gene, an ortholog of CONSTANS of Arabidopsis, was reported in foxtail millet41,42. Although JP71640 is wild type and JP73913 is a splicing variation according to Fukunaga et al.42, no QTL was detected in this analysis. This suggests that the splicing variant of HD1 may not contribute to the DTH between the two parents. Further analyses of genes involved in DTH and interaction between the genes are required to understand adaptation of foxtail millet to various ecological condition of Eurasia in detail.

TEs have been reported to play important roles in foxtail millet domestication and diversification, for example, MITE insertion upstream of the Sh1 gene19 and Copia insertion in the SvLes1 gene5 involved in seed shattering, insertion of 11 different TEs in waxy genes involved in the control of amylose content in endosperm36,37, Harbinger transposon, and LINE insertion in the Si7PPO gene involved in phenol color reaction38. In addition to these genes, DTH was drastically changed by TE insertion in SiPRR37, and leaf sheath color was also changed by multiple independent insertions of Copia TEs in the C gene. It seems that several TEs were involved in the domestication and diversification of foxtail millet. Further analysis of genome-wide TE insertions will enable an in-depth understanding of crop evolution in foxtail millet. Analysis of active TEs will also be useful in reverse genetics in foxtail millet and S. viridis as used for transposon-tagging in maize and rice43,44.


Ethics statement

The authors declare that all methods were performed in accordance with the relevant guidelines and regulations. The test materials were provided by NARO Genebank, Japan, Iwate Agricultural Research Center (IARC), Japan, USDA and Dr. Katrien Devos, University of Georgia, Athens (UGA). We obtained permission from the Genabank, IARC, USDA and UGA to use these accessions.

Plant materials and mapping population

We used a Taiwanese landrace (NARO Genebank JP 73913) that has spikelet-tipped bristles (stb) phenotype45, green leaf sheath, and heading in early-middle August was used as the maternal parent (Fig. 1). This landrace is the only accession with spikelet-tipped bristles among foxtail millet collections in the NARO Genebank, although this trait was reported in a collection of foxtail millet in India46, and is a naturally occurring mutant in a Japanese Setaria viridis population, as shown later. A Japanese landrace (JP71640) with wild-type bristles, red leaf sheath, and heading in early September (Fig. 1) was used as a pollen donor. The F2 population was obtained as described by Sato et al.27, and recombinant inbred lines (RILs) were constructed by a single seed descent (SSD) method47,48. In this study, we used 90 individuals of RIL (F9/F10) populations for linkage map construction and QTL mapping.

For whole-genome sequencing, we also used Otsuchi10 and Nisatai-zairai in addition to JP73913 and JP71640. These accessions are breeding materials for foxtail millet in Iwate Prefecture in the northern part of Japan.

A naturally occurring stb mutant of the wild ancestor, S. viridis, was discovered by TO in Kumihama, Kyotango City, Kyoto Prefecture and designated as ‘Kyoto stb-1’ mutant. The ‘Kyoto stb-1’ was used for an allelism test of the gene in F1 hybrid with JP73913. We crossed the ‘Kyoto stb-1’ with Yugu1 (standard accession of foxtail millet for reference sequence3) after checking the complementation of the gene with JP73913, and developed F2 and F3 populations by self-pollination.

We used 99 accessions of foxtail millet and 6 accessions of S.viridis for genotyping of SiPRR37 gene (Supplementary Table S3). All the foxtail millet accessions except two Japanese accessions (Otsuchi10 and Nisatai-zairai) and Yugu1 were provided by NARO Genebank, Japan. Otsuchi10 and Nisatai-zairai were provided by Iwate Agricultural Research Center (IARC) and Yugu1 was provided by Dr. K. Devos, University of Georgia, Athens, USA. All the six accessions of S.viridis were provided by USDA.

Cultivation of RILs and the investigation of traits

In 2018, 2019, and 2020, we cultivated parents and RILs in the Experimental Farm, Field Science Center, Prefectural University of Hiroshima, Shobara, Hiroshima, Japan (34.83°N, 132.98°E). In 2018 and 2020, six individuals for each line were cultivated in pots, and in 2019, 13–14 individuals were cultivated in a greenhouse (15 cm between individuals in a row and 30 cm between rows) under natural day length. Seeds were sown on June 6, 2018, May 23, 2019, and June 4, 2020, respectively. The heading date was checked as described by Fukunaga et al.42. Stb and leaf sheath color were checked according to Sato et al.27.

DNA extraction

For genotyping, Sanger sequencing, and Illumina sequencing, we used the DNeasy Plant Mini Kit (QIAGEN) for DNA extraction according to the supplier’s recommendations. To extract high molecular weight DNA from leaf tissue for nanopore sequencing, we used NucleoBond HMW DNA (Takara) with some modifications. After DNA extraction, low molecular weight DNA was eliminated using the Short Read Eliminator Kit XL (Circulomics). DNA of F3 individuals derived from a cross between Yugu1 and ‘Kyoto stb-1’ was extracted from dried leaves using a buffer containing 0.2 M Tris-HCl, 0.25 M NaCl, 25 mM EDTA, and 0.5% SDS followed by 2-propanol precipitation38.

Flexible ddRAD-seq and RIL genotyping

We used flexible ddRAD-seq to construct a linkage map49. We designed all enzymatic reactions to be completed sequentially without DNA purification in each step to make the procedures simple49. Additionally, we designed 92 sets of indexed and forked sequencing adaptors compatible with Illumina platform sequencers. The RAD-seq reads were qualified using Trimmomatic (ver. 0.39)50. Only ‘paired’ output reads were retained, and the read sizes used in the subsequent analysis were approximately 742 Mb in JP73913, 758 Mb in JP71640, and 441–830 Mb in RILs. These reads were mapped onto the reference genome of Setaria italica (Accession: PRJNA32913, Assembly: GCF_000263155.2, Cultivar: Yugu1)3 using the ‘bwa mem’ command in BWA (ver. 0.7.12)51. SNP-based genotypes for JP73913 and JP71640, and each RIL was obtained as a variant call format (VCF) file. The VCF file was generated from BAM files of JP73913, JP71640, and each RIL using SAMtools (ver 1.5)52, and the VCF variants were called and filtered using BCFtools (ver 1.5)52. Presence/Absence-type genotypes are also called by the following method: First, the VCF file was generated from BAM files of JP73913 and JP71640 and selected the region where either JP73913 or JP71640 had sufficient read depth (≥ 8) and that the other parental line had no read depth in that region. Next, BEDtools (ver 2.26)53 converted continuous positions in the VCF file to a feature, and only sufficiently wide features (width ≥ 50 bp) were retained as the BED file. For these regions in the BED file, the RIL genotypes were classified into three categories (depth ≥ 2, depth = 0, others) and three genotypes (“existence,” “absence,” “NA”). In this study, we rejected the features with a high percentage of ‘NA’ (0.3 or higher). Additional details are provided in the Supplementary Methods section.

Linkage map construction

For the segregation distortion analysis in each marker using the genotypes obtained in the previous section, the Chi-square test was used to calculate the deviation from the expected ratio (1:1) for each marker. The significance level was adjusted using the Bonferroni correction to account for multiple comparisons. Markers that fit the 1:1 expected ratio and markers that did not fit the expected ratio were used to construct the linkage group separately. The genetic linkage maps were constructed using MSTmap54 with the following parameters: “population_type RIL10; distance_function kosambi; cut_off_p_value 0.0000000000002; no_map_dist 15.0; no_map_size 0; missing_threshold 0.25; estimation_before_clustering no; detect_bad_data no; objective_function ML.” The linkage groups were visualized by the R/qtl package55. The number of linkage groups was the same as that used in the S. italica reference genome3.

QTL analysis

QTL analysis for days to heading (DTH) was performed using the composite interval mapping (CIM) function of the R/qtl package55 with the Haley–Knott regression method56. For the qualitative traits, leaf sheath color, and spikelet-tipped bristles (stb), QTL analysis was performed using the scanone function with option “model = binary.” The LOD significance threshold for detecting QTLs was calculated by performing 1,000 iterations using the R/qtl permutation test. The position and effect of significant QTLs were assessed for percentage phenotypic variation explained (PVE%) by fitting a model containing all QTLs identified for a given trait in R/qtl.

de novo assembly of S. italica accessions

Sequencing of the RIL parents (JP71640 and JP73913) and two other landraces, Otsuchi10 and Nisatai-zairai from Iwate Prefecture, Japan, were carried out using Illumina HiSeq X for short reads and Nanopore MinION (R9.4 flow cell) for long reads. Base calling of nanopore long reads was performed on FAST5 files using Guppy (ONT, UK). The nanopore long reads, which were converted to FASTQ format, were subsequently assembled using NECAT57. To further improve the accuracy of the assembly, Racon58 was used twice, and Medaka (ONT) was subsequently used to correct misassembly. Following this, one round of consensus correction was performed using BWA51 and HyPo59 with Illumina short reads. Finally, we obtained the target gene sequences of the four landraces from each de novo assembly using BLAST60. Target gene sequences of four landraces and Yugu1 were retrieved from the whole genome sequences and aligned with the A10.1 S. viridis reference sequence using BioEdit61 and Clustal W62.

Allelism test and segregation of stb1 in Setaria viridis

For stb1, we tested allelism with a naturally occurring stb mutant of Setaria viridis, ‘Kyoto stb-1.’ ‘Kyoto stb-1’ was crossed with JP73913 showing stb trait in 2012. ‘Kyoto stb-1’ was used as a pollen donor and JP73913 was used as a female parent. F1 was cultivated in pots in 2013, and the bristles were investigated.

HOX14 gene of ‘Kyoto stb-1’ was amplified by a primer combination hbxF1and hbxR3 and sequenced using hbxF1, hbxR3, and internal primers (Supplementary Table S4). ‘Kyoto stb-1’ was also crossed as a pollen donor with Yugu1, a maternal parent and F1 seeds were obtained. F2 and F3 populations were also developed in a greenhouse at the Prefectural University of Hiroshima. We confirmed that this trait was controlled by a single gene in the F2 population. An F3 population was developed and segregation of bristles and an SNP at position + 444 of HOX14 gene (‘C’ for Yugu 1 and ‘A’ for Kyoto stb-1) was investigated. Genotyping of 92 individuals of the F3 population and parents was carried out using the Kompetitive Allele Specific PCR (KASP) genotyping assay (LGC Genomics). Two labeled forward primers, SihbxF-C and SihbxF-A and a reverse primer, SihbxR (Supplementary Table S4) was used for KASP genotyping assay A SNP ‘A’ was labeled with HEX whereas ‘C’ was labeled with FAM, and genotyping was carried out at LGC Genomics, UK.

Geographical distribution of the TE insertion-type SiPRR37 gene

To investigate the TE-insertion type of SiPRR37 in 99 foxtail millet landraces covering a broad traditional cultivation area in Eurasia, including two parents of RILs, Yugu1, Otsuchi10, and Nisatai-zairai and six green foxtail accessions from various parts of the world (two each from Russia and one each from Kazakhstan and Chile) (Supplementary Table S3), we designed primer combinations as shown in Fig. 7a. For the TE insertion type, a ca. 300-bp band was amplified by a primer combination PRR37F1 and PRR37TER1 and a ca. 600-bp band was amplified by a primer combination PRR37F1 and PRR37R1 (Fig. 7a, Supplementary Table S4, Supplementary Fig. S6). PCR conditions were as follows:5 min at 94 °C; 35 cycles of 1 min at 94 °C, 1 min at 60 °C, and 1 min at 72 °C; and 5 min at 72 °C. Toyobo Quick Taq was used for the amplification. PCR products were run on a 1.2 % agarose gel and visualized under UV light with EtBr staining.