Identification and characterization of WOX genes
To identify the putative WOX genes in B. napus and its diploid progenitors, 15 WOX protein sequences of Arabidopsis were acquired and used as query sequences to search against the BRAD database  using the BLASTp program . As a result, 28, 24 and 62 genes were selected as original candidate genes in B. rapa, B. oleracea and B. napus, respectively. Then, the syntenic genes were searched in the BRAD database by inputting the gene IDs of the WOX genes in Arabidopsis, which is a supplement for the first method. As a result, an additional five genes were also identified as WOX genes in B. oleracea. Then, three public protein databases (Pfam, SMART and CDD database) were used to search the HB domain in protein sequences encoded by candidate WOX genes, and proteins that did not contain the complete conserved HB domain were removed. Finally, 25, 29 and 52 genes were identified as WOX genes in B. rapa, B. oleracea and B. napus, respectively. It was clear that the total WOX genes in two diploid progenitors, B. rapa and B. oleracea, was higher than that in the allotetraploid B. napus, which indicated that a gene loss event might have occurred in the WOX gene family of B. napus during polyploidization.
These identified WOX genes in B. napus and its diploid progenitors were named, i.e., from BrWUSa to BrWOX14b in B. rapa, BoWUSa to BoWOX14c in B. oleracea and BnAWUSa to BnAWOX14e in B. napus, according to the homologous relationship with corresponding WOX genes in Arabidopsis (Additional file 1: Table S1). The last lowercase letter in the name represents the degree of homology to the corresponding gene in Arabidopsis, with ‘a’ representing the highest homology, followed by ‘b’, and so on. In B. napus, the capital letters A and C following ‘Bn’ represent the An and Cn subgenomes, respectively. The length of the WOX protein sequences ranged from 133 (BnAWOX14e) to 397 (BnCWOX9a) amino acids in B. napus. In addition, the physical and chemical characteristics of a total of 106 WOX proteins were analyzed and provided, including the molecular weights (MW), theoretical PI values, instability index (II), grand average of hydropathicity (GRAVY) and aliphatic index (Additional file 1: Table S1). The average values of these physical and chemical characteristics were approximately equal to each other in B. napus and its diploid progenitors upon calculation.
Phylogenetic analysis and gene structure analysis
WOX proteins from typical monocots (rice) and dicots (Arabidopsis) were used as reference proteins to construct the WOX phylogenetic tree, where WOX proteins in rice were identified by the same methods mentioned above. Therefore, the unrooted phylogenetic tree was constructed based on a total of 135 WOX protein sequences, including 15 in Arabidopsis, 25 in B. rapa, 29 in B. oleracea, 52 in B. napus and 14 in rice members (Fig. 1). Evidently, the phylogenetic tree showed that WOX proteins were classified into three clades, which were the ancient clade, intermediate clade and WUS clade. According to statistical analysis, the number of WOX proteins in the WUS clade (70) was greater than the sum of proteins in the ancient clade (26) and the intermediate clade (39). Hence, the WUS clade was the largest clade of the WOX proteins in these five species. Notably, WOX proteins in B. napus and its diploid progenitors were related to their corresponding homologs in Arabidopsis or rice in each clade, which suggested that the evolutionary relationship of WOX transcription factors is very close in these species.
For exploring more characteristics about WOX proteins in each clade, WOX protein sequences within the three clades were selected separately to build three phylogenetic trees (Fig. 2). The protein sequences in each clade were similar to each other, whether they were proteins among allotetraploid B. napus or its diploid progenitors. The ancient clade consisted of WOX13 and WOX14, while the intermediate clade consisted of WOX8, WOX9, WOX11, and WOX12, and the WUS clade consisted of WUS and WOX1–7. Interestingly, the homolog of WOX10 could not be found either in B. napus or its diploid progenitors. In addition, exon/intron structures were analyzed to show the structural diversity of WOX genes in different clades and to explore whether the gene structure changed during the polyploidization process (Fig. 2). The results showed that most of the genes had three exons in both the ancient clade and intermediate clade, while 21 genes had two exons, and 19 genes had three exons in WUS clade. By comparison, we found that the gene structure of WOX genes from the WUS clade was significantly more conserved than that of the other two clades during allotetraploid B. napus formation. Six out of eight kinds of WOX genes in the WUS clade had the same gene structure, namely, WOX1, WOX2, WOX3, WOX4, WOX5 and WOX7, whether they were from allotetraploid B. napus or its diploid progenitors. In addition, if two genes that came from the allotetraploid and one of its two diploid progenitors branched at the same final level in the phylogenetic tree, they may have a direct evolutionary relationship. Statistical analysis showed that a total of 33 pairs of WOX genes were found that may have direct evolutionary relationships in these three phylogenetic trees (Table 1). Five out of seven pairs of WOX genes (approximately 71%) in the ancient clade, six out of eleven pairs (approximately 55%) in the intermediate clade and 12 out of 15 pairs (80%) in WUS clade had the same number of exons (Table 1). Thus, 23 out of the 33 gene pairs (approximately 70%) maintained the same gene structure during the formation of B. napus. Therefore, WOX genes were conserved at the DNA level during polyploidization. Furthermore, the location of the HB domain was visualized to facilitate the analysis of the changes in the domain’s position between different clades or different species (Fig. 2). The HB domain of many WOX proteins was located in the N-terminus of the protein in both the intermediate and WUS clades but was located in the middle part of the protein in the ancient clade. We could also see that the length and position of the HB domain were generally conserved. In addition, the MEME website was used to predict conserved motifs in WOX proteins (Fig. 2), and the results showed that at most nine motifs were found in WOX proteins, and only motif 1 was found in every WOX. In general, the WOX gene family in B. napus and its diploid progenitors was very conserved at the DNA and protein level, which might be related to the important function of the WOX genes in these species.
Conserved amino acid sequences within the homeobox domain
The WOX gene family is a plant-specific gene family, of which the typical characteristic is that every WOX protein encoded has a completely conserved HB domain [1, 2]. To study the sequence of the conserved HB domains and the degree of their conservation in different Brassicaceae species, multiple sequence alignment was used to generate the protein sequence logos in B. rapa, B. oleracea, B. napus and Arabidopsis (Fig. 3). The sequence logos showed that the amino acids and their distribution in the HB domain were remarkably similar in these four plants. The HB domain contained one loop, one turn and three helix structures and consisted of 57 amino acids, which was consistent with previous research results . Amino acids in the helix structure were more conserved than those in the loop and turn structure, and the most conserved region was helix3, in which ten highly conserved amino acids were contained, such as I, N, Y, and F. In short, the HB domain was still highly conserved in both B. napus and its diploid progenitors.
Chromosomal localization and orthologous gene analysis of WOX genes
The positions of the identified WOX genes were drafted to chromosomes by using MapInspector software. Ultimately, 25 WOX genes were located on 10 chromosomes in B. rapa (Fig. 4a). Evidently, there is only one WOX gene on chromosome Ar04, three on Ar02 and Ar09, four on Ar03 and Ar05, and two genes on each of the remaining five chromosomes. Twenty-four WOX genes were located on nine chromosomes in B. oleracea, and the other five genes were located on different scaffolds because they had not been assembled into chromosomes (Fig. 4b). Five genes were distributed in chromosome Co02, but in contrast, only one gene was in Co01, Co06 and Co08. Forty-three WOX genes were located on 18 instead of 19 chromosomes in B. napus, and the other nine genes were located on scaffolds (Fig. 4c). It is worth mentioning that no single gene was located on chromosome Cn06 in B. napus. Comparison of the gene distribution of B. napus with B. rapa and B. oleracea showed the important result that many WOX genes retained their relative position in Ar and An, but in contrast, only a few genes retained their relative position in Co and Cn during the formation of B. napus. For example, each pair of chromosomes contained WOX genes with the same number and same location, such as Ar01-An01, Ar04-Ar04, Ar06-Ar06, Ar07-Ar07 and Ar08-Ar08, and other chromosome pairs contained WOX genes with different numbers but similar locations. However, only one chromosome pair, Co02-Cn02, contained WOX genes with the same number and same location. Statistical analysis shows that 21 out of 25 WOX genes (84%) were positioned on the assembled chromosomes in B. rapa, while 12 out of 24 (50%) in B. oleracea maintained their relative position during the formation of B. napus. In combination with previous studies, there are two possible reasons for this result. One possibility is that the Cn subgenome had more abundant TEs than the An subgenome . The presence of TEs in the genome could cause the rearrangement of chromosomal sequences, which affects the genomic structure, such as deletion, inversion, and translocation . The other possibility is that the Cn subgenome underwent more active homologous exchanges (HEs) than the An subgenome during polyploidization . HEs refers to the replacement of some chromosomal regions with duplicated copies of the corresponding fragments of the homologous subgenome , and this event was found to occur frequently between the two subgenomes of B. napus during the hybridization and polyploidization process .
Synteny and duplicated gene analysis of WOX genes
Synteny analysis of WOX genes in B. napus and its diploid progenitors was performed to visualize the locus relationship of homologous WOX genes among two genomes (Ar & Co) and two subgenomes (An & Cn). As shown in Fig. 5, two genes linked to each other by one line were syntenic genes, and genes linked by lines of the same color represented the same kind of WOX gene, such as WOX1 and WOX2. Thus, we can see that many chromosomes in all four genomes/subgenomes (Ar, Co, An and Cn) were connected by the same colored line, which indicated that these genomes/subgenomes were evolutionarily related and the WOX genes were so important that most of them were preserved during polyploidization. In addition, WOX genes were evenly distributed in these four genomes/subgenomes (Fig. 5). Moreover, the synteny analysis indicated that the syntenic WOX gene pairs were widely distributed on the genomes of B. napus and its diploid progenitors.
Moreover, to explore whether Darwinian positive selection affected the evolution of the WOX genes in B. napus and its diploid progenitors, BLASTn  and syntenic gene search in BRAD database  were used to identify duplicated genes among them. As a result, 13, 10 and 38 segmental duplicated WOX gene pairs in the B. rapa, B. oleracea and B. napus genomes were found respectively. Then, the nonsynonymous (Ka), synonymous (Ks) and Ka/Ks ratios were calculated to estimate the selection pressure among duplicated WOX gene pairs. Ka/Ks = 1 means that genes were undergoing a neutral evolutionary process; Ka/Ks > 1 or Ka/Ks < 1 indicate that genes were selected positively or undergoing purified selection, respectively . The Ka/Ks values of all duplicated WOX gene pairs in B. napus and its diploid progenitors were below one (Additional file 2: Table S2), except one duplicated gene pair (BnAWOX11b & BnCWOX11b) had no Ka/Ks value in B. napus because these two genes had the same sequence.
Transposable element analysis of WOX proteins
TEs are widely distributed in the genome, and many transposons are located near the host genes . To investigate whether TEs were involved in the expansion of the WOX gene family, we identified the TEs located 2000 bp upstream and downstream of the WOX genes using the homolog search method . Compared to the TEs near the WOX gene family in cotton , there were more TEs in both B. napus and its diploid progenitors (Table 2). After analysis, 402, 202 and 235 TEs were found in B. napus, B. rapa and B. oleracea, respectively. Thus, a conclusion can be drawn that as early as the formation of the diploid progenitors of B. napus, the WOX gene family has undergone significant expansion due to the presence of abundant TEs. The three most abundant types of TEs in order of abundance are DNA transposon, LTR retrotransposon and non-LTR retrotransposon. Two types of TEs, Ginger/TDD and R1, were located downstream of BnAWOX3b and BnCWOX12a, respectively, but these two TEs were not detected near the WOX genes in the diploid progenitors. As shown in Table 2, there are 21 kinds of DNA transposons near the WOX genes. The most abundant ones are EnSpm/CACTA, MuDR, hAT, Helitron, Mariner/Tc1 and Harbinger. LTR retrotransposons near the WOX genes mainly contained four types, Gypsy, Copia, BEL and DIRS. Furthermore, there were 18 kinds of non-LTR retrotransposons near the WOX genes of selected species, and the most abundant kind was the L1 type. Statistical analysis shows that 23, 14 and 18 L1-type transposons were found near the WOX genes of B. napus, B. rapa and B. oleracea, respectively, and the number of L1-type transposons was much higher than the number of other non-LTR retrotransposons in these species. Compared to TEs, simple repeats were less abundant in B. napus and its diploid progenitors. Specifically, there were two simple repeats in B. napus, but only one in B. rapa and none in B. oleracea.
Gene expression pattern analysis of WOX genes
To gain insights into the putative biological functions of WOX genes, we investigated their expression patterns in four tissues (leaves, stems, flowers and siliques) of B. napus and its two diploid progenitors based on our RNA-seq data (Additional file 3: Table S3). As shown in Fig. 6, we found that WOX genes are widely expressed in these four tissues, suggesting that WOX genes have multiple biological functions and operate in different tissues. In addition, the expression of WOX genes from different clades had different characteristics, and the specific characteristics were as follows: The genes of the intermediate clade were generally not expressed in all tissues, except BrWOX9a and BnCWOX9a, which were expressed in flowers; In the ancient clade, most of the WOX13 homologous genes were widely expressed in the four tissues and had a high expression level, and WOX14 homologous genes were not expressed in flowers; In the WUS clade, only the homologous genes of WOX4 were widely expressed in the four tissues. WOX3 and WOX6 homologous genes were not significantly expressed in all four tissues except BnCWOX3a, BoWOX3a, BnAWOX6a and BoWOX6b, which were detected in flowers. In addition, the homologous genes of WOX1 generally were not expressed in stems of B. napus or its two diploid progenitors. In brief, the most active genes were the genes in the ancient clade; conversely, the least active genes were those in the intermediate clade in B. napus and its two diploid progenitors, which suggested that WOX genes in the ancient clade play important roles in the process of growth and development of B. napus and its two diploid progenitors.
To explore whether the expression pattern of the WOX genes in the four tissues changed in allotetraploid B. napus and its two diploid progenitors, we selected the previous 33 pairs of genes that may have evolutionary relationships for analysis. As shown in Table 3, the fragments per kilobase of exon per million reads mapped (FPKM) values of the 33 gene pairs with potential direct evolutionary relationships were collected. As a result, we found that there was no direct relationship between the same gene structure and the same expression trend in these gene pairs. For example, 13 out of the 23 (approximately 56%) gene pairs with the same gene structure had absolutely different expression trends in the four tissues, such as BoWOX13a & BnCWOX13c and BoWOX4a & BnCWOX4b. However, 4 out of 10 (40%) gene pairs with distinct gene structures had the same expression trend, such as BoWOX12b & BnCWOX12a and BrWOX11b & BnAWOX11d. These results suggested that many WOX genes have no obvious changes at the DNA level, but most of the genes presented different characteristics at the expression level, which might be caused by the changes in gene expression regulation in the process of polyploidization.
Bias expression analysis of WOX genes
To explore the expression bias of WOX genes in allotetraploid B. napus in different tissues, bias analysis was performed based on FPKM. The 33 previously selected WOX gene pairs could be grouped according to homology, so there were 12 groups of WOX genes, such as WOX14, WOX3 and WUS. Since two groups of genes (WOX11 & WOX5) were present in only one diploid progenitor, the bias analysis cannot be performed on these genes. Therefore, we selected the remaining 10 groups of WOX genes for bias analysis.
The expression bias of the WOX genes showed different characteristics in different tissues. As shown in Additional file 4: Table S4, in flowers, the expression of 9 groups of WOX genes were biased towards B. rapa, and only the expression of WOX12 was biased towards B. oleracea. In leaves, the expression of 7 groups of WOX genes was biased towards B. rapa, and only the expression of WOX14 was biased towards B. oleracea; additionally, the expression of two other groups of genes (WOX6 & WOX8) had no obvious bias. In stems, the expression of 6 groups of WOX genes was biased towards B. rapa, and the expression of two groups of genes (WOX4 & WOX14) was biased towards B. oleracea; additionally, two groups of genes (WOX6 & WOX8) had no obvious bias. In siliques, the expression of 4 groups of WOX genes was biased towards B. rapa, while 5 groups of WOX genes were biased towards B. oleracea, and only WOX6 had no obvious bias.
Hence, the expression bias of WOX genes in stems and leaves was largely identical to each other, except that the expression of WOX4 was biased towards B. rapa in leaves, while biased towards B. oleracea in stems. The expression of WOX6 had no bias in stems, leaves and siliques but was biased towards B. rapa in flowers. The expression of WOX14 was biased towards B. oleracea in stems, leaves and siliques. Three groups of genes (WUS, WOX3 and WOX13) were biased towards B. rapa in all four tissues. In general, the results showed that the expression of WOX genes in B. napus was biased towards B. rapa in stems, leaves and flowers, while they had no obvious bias in siliques.