Breeding histories and selection criteria for oilseed rape in Europe and China identified by genome wide pedigree dissection

Selection breeding has played a key role in the improvement of seed yield and quality in oilseed rape (Brassica napus L.). We genotyped Tapidor (European), Ningyou7 (Chinese) and their progenitors with the Brassica 60 K Illumina Infinium SNP array and mapped a total of 29,347 SNP markers onto the reference genome of Darmor-bzh. Identity by descent (IBD) refers to a haplotype segment of a chromosome inherited from a shared common ancestor. IBDs identified on the C subgenome were larger than those on the A subgenome within both the Tapidor and Ningyou7 pedigrees. IBD number and length were greater in the Ningyou7 pedigree than in the Tapidor pedigree. Seventy nine QTLs for flowering time, seed quality and root morphology traits were identified in the IBDs of Tapidor and Ningyou7. Many more candidate genes had been selected within the Ningyou7 pedigree than within the Tapidor pedigree. These results highlight differences in the transfer of favorable gene clusters controlling key traits during selection breeding in Europe and China.

In B. napus most traits affecting yield and quality have a complex polygenic basis [11][12][13][14] . Mapping of quantitative trait loci (QTL), which is used to identify genomic regions that are responsible for trait variation, is based on associations between polymorphic markers and phenotypic values 13,14 in unselected biparental segregating populations. This method can reveal the genetic basis of complex traits for which prior knowledge may be limited and the lack of which would otherwise present a major constraint to crop breeding 15 . The BnaTNDH mapping population was generated through anther culture of the F 1 generation of a cross between Tapidor and Ningyou7 16 . Within this population, five to 18 QTLs for flowering time have been detected in 12 winter microenvironments and three spring microenvironments, with about 60% of the phenotypic variation for flowering time attributed to genetic effects 17 . A QTL on linkage group A10, qFT10-4, was detected in a spring-cropped environment. BnaA. FLC.10 has been identified as a candidate gene that has been shown to be an important determinant of winter versus spring type OSR 17 . In another study with the same population grown in ten environments across three geographic regions 18 , 437 SNPs associated with flowering time were detected, some of which were associated with known genes such as orthologs of APETALA1 in A. thaliana. Genetic loci contributing to seed erucic acid content 11-14, 16, 19 , seed and leaf glucosinolate content 14,20,21 , and root traits affecting phosphorus (Pi) acquisition 22,23 have also been identified in B. napus by QTL mapping or through genome wide associated studies (GWAS).
Identity by descent (IBD) refers to a haplotype segment of a chromosome inherited from a shared common ancestor 24 . IBD segments have been employed to determine the origin of low diversity regions in humans to detect rare alleles related to diastolic blood pressure 25 . Selection tends to increase the number of IBD segments among individuals in a population. Strong and very recent selection in the human genome has been identified by scanning regions with excess IBD sharing 26,27 .
Based on the differences between the number of segregating sites and the average number of nucleotide differences, Tajima's D test can be used to distinguish a DNA sequence diverging randomly from another that is diverging due to a non-random process, including directional selection or balancing selection, demographic expansion or contraction, genetic hitchhiking or introgression 28 . In maize, Tajima's D test has been used to establish the genome location(s) where selection has occurred 29 . When compared with long term selection in natural environments, domestication promotes rapid phenotypic evolution through artificial selection 30 . Random genetic drift is a powerful mechanism that enables populations of finite size to acquire genetic structure 31 . This can be seen in the domestication bottleneck and associated reduction in genetic diversity for specific target genes subject to artificial selection, with the magnitude and variance of this reduction across loci providing insights into the demographic history of domestication 32 .
In this study, homozygous lines derived from Tapidor, Ningyou7 and their ancestors were screened using the genome-anchored Brassica 60 K Illumina Infinium SNP array. The objectives were (1) to survey IBD regions in the pedigree of these cultivars to identify differences in the extent of IBD transfer from their ancestors to offspring; (2) to identify candidate genes underlying QTL within IBD regions for flowering time, seed quality and root morphology traits and uncover any gene clusters transferred from the progenitors to Tapidor and Ningyou7, (3) to identify the genome regions where breeding selection has occurred using Tajima's D and gene diversity tests.  Table S1). C03 was the longest chromosome, represented by ~60.5 Mb in the Tapidor and Ningyou7 pedigrees and ~60.6 Mb in cultivar Darmor-bzh, while A10 was the shortest chromosome, with ~17.4 Mb in both the Tapidor and Ningyou7 pedigrees as well as Darmor-bzh (Fig. 2). For all 19 chromosomes, the lengths represented within the Tapidor and Ningyou7 pedigrees were slightly shorter than those of Darmor-bzh. The total length of the A subgenome (A01 to A10) was 238.8 Mb and of the C subgenome (C01 to C09) 404.9 Mb (Supplementary  Table S1). An average density of 46 SNP per Mb was recorded in the genomes of the Tapidor and Ningyou7 pedigrees. Compared with other chromosomes, SNP marker densities were lower in A02 (30 SNP per Mb), C05 (20) and C09 (22) (Supplementary Table S1).  (Fig. 2).

SNP distribution in the
Most pairwise comparisons of cultivars detected more IBD blocks in the A subgenome than in the C subgenome, e.g. Bronowski vs Tapidor, Regent vs Tapidor, Bienvenu vs Tapidor, Shengliyoucai vs Ningyou7 and Ningyou1 vs Ningyou7 (Fig. 2). In contrast, there were fewer IBD blocks in the A subgenome for Liho vs Regent, Liho vs Tapidor and Ningyou7 vs Chuanyou2 (Fig. 2). No significant difference between subgenomes was observed for Bronowski vs Regent and Shengliyoucai vs Chuanyou2 (Fig. 2). The total lengths of the IBD blocks were shorter in the A subgenome than in the C subgenome for all pairwise comparisons of cultivars apart from Bronowski vs Tapidor. Overall the A subgenome showed more genetic variation than the C subgenome.
Within the Tapidor pedigree, the progenitor cultivar comparison of Bronowski vs Regent had the most (48) and longest (158.4 Mb) IBD blocks, whilst Liho vs Tapidor had the least (6), and shortest (6.6 Mb) IBD blocks (Fig. 2). Within the Ningyou7 pedigree, Ningyou1 vs Ningyou7 had the most (77), and Chengduai vs Chuanyou2 the least (2) and shortest (5.9 Mb) IBD blocks, while Chunayou2 vs Ningyou7 had the longest (417.7 Mb) IBD blocks ( Fig. 2 and Supplementary Table S2). These results suggest that the IBD block length decreases with increasing number of generations and, hence, recombination cycles.
Two paths of haplotype transfer are possible within the Tapidor and Ningyou7 pedigrees, either via direct linear transfer from original parent to progeny in recent breeding crosses, or indirectly by transfer from intermediate parents generated in earlier breeding crosses (Fig. 3 Fig. 3a).
The physical positions corresponding to QTLs identified for flowering time, seed oil content, seed erucic acid content, seed glucosinolate content and root morphology traits were mapped on the genome of the Tapidor and  Table S2). Within the Tapidor pedigree negative values were associated with C09, while in the Ningyou7 pedigree they were associated with two A subgenome chromosomes (A03, A05) and  Table S2). We identified four classes of Tajima D values accounting for the total SNP variation within the Tapidor (T pedigree ) and Ningyou7 pedigrees (N pedigree ), with Class 1 having (−2 to −1): 5% of T pedigree vs 13% N pedigree ; Class 2 (−1 to 0): 20% of T pedigree vs 34% N pedigree ; Class 3 (0 to 1): T pedigree 48% vs 40% N pedigree ; Class 4 (1 to 2): T pedigree 13% vs 13% N pedigree ( Supplementary  Fig. S1).
Gene diversity across all chromosomes was similar for both pedigrees (Supplementary Table S2). In the Tapidor pedigree, mean values ranged from 0.35 (C05) to 0.44 (A04) with a mean of 0.40, compared with 0.3 (A02) to 0.52 (C01) with a mean of 0.36 in the Ningyou7 pedigree. The mean polymorphism information content (PIC) was slightly greater in the Tapidor pedigree (0.34, ranging from 0.28 in C05 to 0.38 in A04) than in the Ningyou7 pedigree (0.31, ranging from 0.24 in A02 to 0.45 in C01) (Supplementary Fig. S2 and Supplementary  Table S2).
Two primary artificial selection processes are apparent in the breeding history of Tapidor and Ningyou7 (Fig. 5). Where a locus has a Tajima's D <0 and gene diversity <0.3 (Fig. 5A), the artificial breeding selection of the locus is more likely to have occurred during the earlier breeding cycles. Where a locus has a Tajima's D <0 and gene diversity >0.3 (Fig. 5B), the artificial breeding selection of the locus is likely to have occurred in a later round of breeding selection. Where a locus has a Tajima's D >0 and gene diversity <0.3 (Fig. 5C), the artificial breeding selection of the locus is more likely to have taken place prior to the founding cultivars. Finally, where a locus has a Tajima's D >0 and gene diversity >0.3 (Fig. 5D), there is no strong evidence for artificial breeding selection occurring at the locus (Figs 5 and 6) 30 . A total of 42 genes, 15 within the Tapidor and 27 within the Ningyou7 pedigrees, were detected where genetic transfer was associated within the earlier breeding selection process ( Fig. 6 and Supplementary Table S2). Among these genes, two for flowering time and one for seed erucic acid content in the Tapidor pedigree appeared to have been subject to breeding selection. In the Ningyou7   Figure 4. Distribution of QTLs detected for flowering time, seed quality and root morphology traits within the BnaTNDH population, and the candidate genes underlying the QTL region located in IBDs of cultivars of the Tapidor and Ningyou7 pedigrees. The outermost circle represents the SNP markers located on the genome of cultivar Darmor-bzh. Circle 'I' indicates the locations of IBD blocks on each of the chromosomes within the Tapdior pedigree; 'IV' within the Ningyou7 pedigree. Circle 'II' represents the additive effect QTLs for different agronomic traits located in the IBD regions within the Tapidor pedigree, and 'V' within the Ningyou7 pedigree. Circle 'III' demonstrates the candidate genes located in the QTL regions within the Tapidor pedigree and 'VI' within the Ningyou7 pedigree. pedigree, the genes involved in breeding selection included five for flowering time, two for seed erucic acid content, three for seed glucosinolate content and two for root morphology and phosphorus uptake. In the later breeding selection process, only two genes in Tapidor, but 116 in Ningyou7 were detected as being associated with genetic transfer (Fig. 6 and Supplementary Table S2). Of these, only one from the Tapidor pedigree and 65 from the Ningyou7 pedigree appeared to have been subject to breeding selection. The sole gene detected within the Tapidor pedigree, BnaA.FAE1, is an ortholog of KCS18 (3-ketoacyl-CoA synthase 18) located on A08, and represents one of the key domestication genes introduced from Liho, and known to contribute to modern 'double-low' canola, by reducing seed erucic acid content. The genes within the Ningyou7 pedigree included 15 for flowering time, ten for oil content, 18 for glucosinolate content, ten for erucic acid content, two for seed protein content, and ten for root morphology and phosphorus uptake ( Fig. 6 and Supplementary Table S2).
Favorable gene clusters transferred in the breeding of Tapidor and Ningyou7. Genetic hitchhiking (linkage drag) effects contribute to linkage disequilibrium (LD) 33 . The LD of the ten cultivars within the Tapidor and Ningyou7 pedigrees was calculated and used to estimate the extent of linkage drag. A mean correlation coefficient (r 2 ) of 0.227 in the pedigree lineage indicated that a significant genetic relationship might exist at the whole genome level. When r 2 = 0.2, the LD decay was 0.7 Mb. Thus, where genes are located within a region of LD ≤0.7 Mb in the B. napus genome they will form a cluster, and are more likely to be transferred as an intact haplotype block from the parents to offspring. A total of 24 favorable gene clusters, 10 in the A subgenome and 14 in the C subgenome were identified. These were associated with seed quality, flowering time, and root morphology traits linked to phosphorus uptake. They were located on all chromosomes apart from A02, C06 and C07 ( Fig. 7 and Supplementary Table S2). Genetic transfer was detected within the Ningyou7 pedigree (18 clusters), the Tapidor pedigree (2 clusters) and within both pedigrees (4 clusters). In addition, 12 gene clusters were associated with combinations of two or more important agronomic traits, such as flowering time, root morphology and phosphorus uptake (No 6, A06), or flowering time and seed oil content (No. 14, C02; No. 20, C05; No. 22, C08) (Supplementary Table S2).

Discussion
Tapidor is a double-low (low seed glucosinolate and low seed erucic acid content) winter B. napus cultivar developed in Europe. Ningyou7 is a double-high (high seed glucosinolate and high seed erucic acid content) semi-winter B. napus cultivar developed in China. The flowering time of Tapidor is later than that of Ningyou7 17 , and has a longer primary root and fewer lateral roots than Ningyou7 23 . Agronomic and seed traits within the pedigrees of both these cultivars have undergone substantial improvement through extensive breeding efforts. These cultivars were crossed to generate the BnaTNDH biparental doubled haploid segregating population, which has been used extensively to understand the genetic basis of many agronomic and economically important traits Colored discs represent the number of key genes originating from each ancestor cultivar that have contributed to: flowering time (yellow), seed oil content (blue), seed glucosinolate content (orange), seed erucic acid content (red), seed protein content (purple), and root morphological traits (pink). Rectangular boxes represent genes that were not transferred to Tapidor and Ningyou7 for flowering time (yellow) and seed erucic acid content (red). The number in parenthesis is the theoretical genetic information transferred from progenitor cultivars to Tapidor and Ningyou7.
in B. napus 1,13,14,16,17,19,23,[33][34][35][36] . Uncovering the associated underlying patterns of allelic variation in the context of the sequenced genome is anticipated to provide valuable knowledge that will guide subsequent advances in breeding 1,11 . In this study, Tapidor, Ningyou7 and their eight progenitor ancestors were screened with the 60 K Brassica Infinium SNP array. A total of 29,347 high-quality SNP markers were mapped to the 19 pseudomolecule chromosomes of Darmor-bzh (Supplementary Table S1). Using the SNP markers of Tapidor and Ningyou7 as the reference for each pedigree, IBD regions detected from pairwise comparisons of cultivars in each of the pedigrees were assessed ( Fig. 4 and Supplementary Fig. S3). The number of IBD blocks for the cultivars in the Ningyou7 pedigree was greater than that in the Tapidor pedigree (Fig. 4), which provides evidence of a greater power of selection or increased recombination occurring in the recent breeding of Ningyou7 [26][27][28] . The IBD regions that Regent inherited from the two grandparents studied here summed to only about 176 Mb (Table 1), only a subset of the 650 Mb covered by the SNP markers (Fig. 4). This can be attributed to Regent having inherited almost 75% of its genome complement from Turret 5 . A similar consequence of complex or unbalanced pedigree construction appears to account for the relatively low level of 202 Mb IBD regions for Tapidor derived from the parents and grandparents studied here ( Fig. 4; Table 1). In this case, Tapidor has derived part of its genome complement from SI8879 as well as from Turret 7 (Fig. 1). Overall, the total IBD length in the C subgenome was larger than that in the A subgenome in both pedigrees (Fig. 4), suggesting that the C subgenome of parental cultivars has contributed more to the selected agronomic traits of current cultivars than the A sub-genome, whether bred in Europe or in China. The relative conservation of the C subgenome during breeding of both Tapidor and Ningyou7 is consistent with observations that i) canola OSR cultivars show less genetic variation in the C compared with A subgenomes 11 and ii) LD decay of canola OSR cultivars is much larger in the C than in the A subgenome 37 .
The QTLs for flowering time, seed oil content, seed glucosinolate content, seed erucic acid content, seed protein content and root morphological traits were reanalyzed using the new high-density SNP-based BnaTNDH linkage map 36 (Luo et al. unpublished data). The QTLs and putative genes located in the IBD regions of cultivars within the Tapidor and Ningyou7 pedigrees illustrate the differences in haplotype transfer from the progenitor cultivars to Tapidor and Ningyou7 ( Fig. 6 and Supplementary Table S2). The 18 favorable gene clusters identified in the Ningyou7 pedigree were involved in six important agronomic traits, while the two favorable gene clusters identified in the Tapidor pedigree were only associated with seed glucosinolate and protein content ( Fig. 7 and Supplementary Table S2). Half of the 24 favorable gene clusters were associated with two or more important agronomic traits, suggesting that agronomic traits such as flowering time and root morphology could influence seed quality traits, including oil, erucic acid, protein, and glucosinolate content 14,23,38 . This might be due to pleiotropic effects when a favourable gene substitution occurs in a population, or due to changes in gene frequencies at closely linked loci 39 .
Genes with lower gene diversity in a population tend to reflect selection in the breeding of cultivars 29,40 . In our study BnaA05g03310D (BnaA.FPA), which is the B. napus ortholog of the flowering time gene AT2G43410  in A. thaliana and Bra004761 in B. rapa (Chiifu-401), was detected within the IBD block on A05 with lower gene diversity in two early breeding cycles in pairwise comparison of progenitor cultivars Chunayou2 vs Shengliyoucai, Ningyou7 vs Shengliyoucai and Ningyou7 vs Chuanyou2 from the Ningyou7 pedigree (Fig. 7). The donor parent of BnaFPA is Shengliyoucai and the gene was transferred via Chuanyou2 to Ningyou7. In south China, early flowering results in early harvest of OSR, which can alleviate loss of seed yield due to high temperatures from late April to early May. Plant roots are of fundamental importance to soil resource acquisition 41 . Phosphorus acquisition can be improved by increasing the lateral roots distributed in the topsoil 42 . An ortholog of AtIAA28 was found within an IBD block on A06 which is conserved from Shengliyoucai to Chuangyou2 and hence to Ningyou7, and is co-located within a QTL for lateral root development ( Fig. 6 and Supplementary Table S2). Genes homologous to AtPht1;9 are found within IBD blocks on A09 conserved from Shengliyoucai to Chuanyou2 in the same pedigree, and are collocated within a QTL for primary root length and seed yield per plants at both low and high phosphorus supply (Fig. 6 and Supplementary Table S2). In the Tapidor pedigree, orthologous alleles of AtPht1;9 were conserved from Bienvenu to Tapidor. Genes that have been subject to breeding selection show lower gene diversity (Supplementary Table S2). The B. napus orthologue of A. thaliana AtPht1;9, BnaA03g35470D, is located on chromosome A03 and has also been detected as a contributor to responses to phosphorus deficiency in a B. napus population of 405 inbred lines (Wang et al., unpublished data). Phosphate fertilizers were used extensively in European agriculture 43 during the period Tapidor was bred from Liho and Bronowski, whilst little phosphate fertilizer was being used in China during the time Ningyou7 was being developed from Shengliyoucai and Chengduai. It is possible, therefore, that differences in root morphology between Tapidor and Ningyou7 23, 36 might be attributed to selective breeding under these contrasting conditions.
Although the Brassica 60 K Infinium SNP array 44 provides a straightforward and powerful platform to facilitate assessment of genetic variation among B. napus cultivars, we recognize that the detection of SNP variation may be biased due to the relatively small number of genotypes that were originally used to identify SNPs. Since sequence data from both Ningyou7 and Tapidor as samples in the development of the SNP array 45 , this could affect the utility of Tajima's D as a measure of the evolutionary history of a locus. In particular, this could occur since Tajima's D is based on detection of pairwise differences between samples. An example of this potential bias is apparent in the detection of only one FAE (KCS18) locus on A08, whereas the corresponding C genome copy on C03 was not detected as a candidate gene, although it had previously been identified in contributing to the low erucic acid phenotype of Tapidor 19 . Moreover, the detection of candidate genes and estimates of gene diversity based on array data does not take into account those polymorphisms that may be present between Tapidor and Ningyou7 but not represented on the array. Based on the transcriptome data of Bancroft et al. (2011) 1 , 19 of 105 candidate genes within IBD blocks and QTL had between 1 and 12 SNPs between Tapidor and Ningyou7 and appear to be associated with the set of traits investigated in our study (Supplementary Table S3). Unfortunately we were not able to differentiate gene homologs as the transcriptome data are not yet anchored to physical map positions 1 . However, the polymorphisms that were discovered could be used to generate molecular markers to assign gene loci to specific QTL regions.
The total IBD block length in the C subgenome was larger than that in the A subgenome in both the Tapidor and Ningyou7 pedigrees, suggesting that the C subgenome had probably contributed more to agronomically useful traits than the A subgenome in the breeding of OSR in both Europe and China. The genetic differences in improved traits (flowering time; seed yield; seed oil, glucosinolate and erucic acid content; and root traits for P uptake) during the breeding history of Tapidor and Ningyou7 have been identified from IBD, QTLs and candidate genes, as well as with Tajima's D and a gene diversity test in the two pedigrees. Twenty four favorable gene clusters were detected as being transferred from the progenitor parents to Tapidor and Ningyou7, and could be used for further improving and dissecting the agronomic traits of B. napus.

Methods
Plant materials. Tapidor pedigree cultivars originate from European countries and Canada. Among these Liho came originally from Germany, Bronowski from Poland, Bienvenu and Tapidor from France, and Regent from Canada. Ningyou7 pedigree cultivars originate from Asian countries, with Shengliyoucai from Japan, and Chengduai, Chuanyou2, Ningyou1 and Ningyou7 from China. The species and geographical origin and basic traits of all cultivars studied are summarized in Supplementary Table S4, and their pedigrees are summarized in Fig. 5. Seeds were provided by Jinling Meng and grown in the field in Wuhan (114°20′54″E, 30°28′36″N) with self-pollination. Traits (seed oil content; seed glucosinolate content; seed erucic acid content; seed protein content) were assessed by near-infrared reflectance spectroscopy (NIR; Systems 5000) 11 and flowering time assessed according to Long et al. 17 . Root traits and phosphorus uptake were evaluated according to Shi et al. and Zhang et al. 23,36 (Supplementary Table S5).

Collection of agronomic traits and QTL mapping. Data collection. Data for flowering time of the
BnaTNDH population and its parental lines, Tapidor and Ningyou7, were mostly obtained from previous studies 17 across 11 environments over four years. Flowering time was calculated as the time from sowing to the date when the first flower of half of the plants in the plot had opened. Lines that did not flower in all the spring-cropped environments were given a score of 150 days 18,46 . Data for seed oil, glucosinolate, erucic acid and protein content of the BnaTNDH population and its two parents were also acquired primarily from previous studies 13, 14 across 15 environments over five years. In these studies approximately 3 g seed per accession were analysed using NIRS on a reflectance scanning mode 14 . Root morphology data for the BnaTNDH population and two parents grown at low phosphorus (LP) and high phosphorus (HP) supply were obtained from a previous study by Shi et al. 23 . The plants were grown at LP (0.006 mM P) and HP (0.625 mM P) supply on agar, with ample supply of all other nutrients.
The trays were scanned at 12 d. Seedling traits, including primary root length, lateral root number, lateral root density, lateral root length, root and shoot fresh weight, were determined. QTL mapping and prediction of candidate genes underlying the QTL regions. All the data for flowering time, seed quality and root morphology traits from the BnaTNDH population were used to conduct QTL analysis using the BnaTNDH 2041 linkage map, a new high-density SNP-based genetic linkage map 36 (Luo et al., unpublished data). QTL detection employed the composite interval method (CIM) using QTL cartographer software version WinQTLCart2.5 47 . SNP markers flanking the QTL regions were mapped on the genome of Darmor-bz 4 . The genes related to the studied traits located in the homologous physical regions of Darmor-bzh were predicted to be the candidate genes.
Genotyping. DNA extraction. A modified cetyltrimethyl ammonium bromide (CTAB) method was used to extract DNA from young leaves 48 . Four leaves from different individuals of each line were used to construct DNA bulks. The DNA concentration in bulks was measured by electrophoresis through a conventional 2% agarose gel. 30 ng μl −1 , 50 ng μl −1 and 100 ng μl −1 λDNA (48502 bp) was used as reference. The final DNA concentration was adjusted to be 50 ng μl −1 .
Microarray hybridization and SNPs identification. The Brassica 60 K Illumina Infinium SNP array (Illumina, USA) contains 52,157 probes, each representing a distinct locus. Microarray hybridization consisted of the following steps: I, The DNA samples were denatured and neutralized to be prepared for amplification; II, The amplified product was fragmented by MSM enzyme; III, After precipitation using isopropanol, the fragmented DNA was collected by centrifugation at 4 °C and the precipitated DNA was re-suspended and in hybridization buffer at 48 °C and denatured at 95 °C; IV, Re-suspended DNA were added to a beadchip for hybridization at 48 °C; V, Using the captured DNA as a template, oligos were extended on the beadchip by a single base; VI, The Illumina HiScan was used to scan the beadchip, using a laser to excite the fluorophore of the single-base extension product on the beads. The scanner recorded high-resolution images of the light emitted from the fluorophores, which were analysed using the Illumina HiSeq 2000. The fluorophores had red and green colors, which represented four different types of SNP marker (A, T, C and G). Genetic loci were identified by statistical analysis (Infinium HD Assay Ultra, Manual, Experienced User Card) 14, 18, 35 . Physical mapping of SNP markers. The Brassica 60 K Illumina Infinium SNP array was designed based on reference sequences of B. rapa (AA) and B. oleracea (CC) 14 . Each of the SNP markers is attached to a length of 50 bp SNP probe. The genome of Darmor-bzh was used as the reference genome and all the SNP markers were mapped to its physical map. Only one copy of BLAST hits of the SNP marker against the reference sequences were considered to be the most likely SNP position 14 .

Identity by descent (IBD) analysis in Tapidor and Ningyou7 pedigrees. Identity by descent (IBD)
is a segment on the chromosome representing a haplotype block inherited from a shared common ancestor 24 . The software fastIBD (Beagle version 4.0) 49 was used to detect IBD between pairs of cultivars among the Tapidor and Ningyou7 pedigrees using genome-wide SNP data. The software takes account of haplotype frequencies and uncertain haplotypes whilst enabling fast computation using genome-wide SNP data. Linked markers were identified at a P value(E) < 10 −9 .
The distributions of IBD regions in Tapidor and Ningyou7 pedigrees were represented using R3.1.3 plotting software 3 . Using SNP markers for Tapidor or Ningyou7 as a reference, IBD regions for pairs of cultivars within the respective pedigrees were mapped. Based on the physical map (anchored genome sequence) of Darmor-bzh, the genes detected both within the QTL regions detected in the BnaTNDH population, and within the IBD region of the progenitors of Tapidor and Ningyou7, were used to identify gene clusters.

Tajima's D test and Gene diversity.
Tajima's D test is used to determine where selection has occurred at the DNA level based on the neutral selection theory of populations 29 . The Dnasp5 software 50 uses a sliding window method (segment of DNA) which progressively scans along the genome sequences in steps, and was employed to calculate parameters across a DNA region. The parameter is calculated in each window, and the value assigned to the nucleotide at the midpoint of the window. The D pair statistic is an estimate of the diversity level of the five cultivars within each pedigree using a sliding windows analysis, and is able to establish the variation of a unit of 15 loci with a single locus at each step 29 .
PowerMarker V3.25 was employed to calculate allelic frequency differences, in order to speculate on the genetic difference due to mutations and selection 29,51 . The genome wide distribution of gene diversity for each of the 19 chromosomes was assessed in the BnaTNDH population. The selection loci in genomes of the Tapidor and Ningyou7 pedigrees were determined by combining the gene diversity test and the candidate genes underlying the QTL regions. A higher frequency of selection events is associated with regions with lower gene diversity. Based on two main breeding selection cycles, the gene diversity changes among three cultivars were calculated. These cultivars were earlier breeding cycle cultivars (Liho, Bronowski and Regent) and later breeding cycle cultivars (Bienvenu, Regent and Tapidor).
Nei's measure of the average gene diversity per locus H S is determined by the formula 30  where k is the total number of loci (differentiating factors), H Ss = 1 − q s 2 − (1 − q s ) 2 , and q s is the frequency of one of the two alleles at the sth diallelic locus (or virulence frequency, or band frequency, or frequency of appearance 1 at the sth differentiating factor).
Linkage disequilibrium (LD). The model of non-linear regression in TASSEL 3.0 14 was used to calculate the LD of whole-genome of the ten cultivars in Tapidor and Ningyou7 pedigrees. The full matrix LD model was chosen and the correlation coefficient (r 2 ) for pairs of markers was calculated using a sliding window with increments of half a window each step 52 . A curved line was fitted based on X (r 2 ) and Y (physical distance) and r 2 was 1 while physical distance of two loci equal to 0 bp. When r 2 fell below 0.2, the physical distance was estimated 53 . Where genes are located within a region of linkage disequilibrium (LD ≤ 0.7 Mb) in the B. napus genome they will form a cluster, and are more likely to be transferred as an intact haplotype block from the parents to offspring.