Origin and evolution of the Rax homeobox gene by comprehensive evolutionary analysis

Rax is one of the key transcription factors crucial for vertebrate eye development. In this study, we conducted comprehensive evolutionary analysis of Rax. We found that Bilateria and Cnidaria possess Rax, but Placozoa, Porifera, and Ctenophora do not, implying that the origin of the Rax gene dates back to the common ancestor of Cnidaria and Bilateria. The results of molecular phylogenetic and synteny analyses on Rax loci between jawed and jawless vertebrates indicate that segmental duplication of the Rax locus occurred in an early common ancestor of jawed vertebrates, resulting in two Rax paralogs in jawed vertebrates, Rax and Rax2. By analyzing 86 mammalian genomes from all four major groups of mammals, we found that at least five independent Rax2 gene loss events occurred in mammals. This study may provide novel insights into the evolution of the eye.

Acquiring visual information from the external environment is critical for animal survival. Over the course of evolution, animals have developed different kinds of eyes, from eyespots to complex refractive and compound eyes, which allow them to respond to light stimulus [1]. Notably, vertebrates have developed camera eyes, in which the retina receives the visual input [1].
The homeobox gene superfamily encodes transcription factors with diverse functional roles [2]. For DNA recognition, these transcription factors share a 60-amino-acid homeodomain, which comprises a helix-turn-helix structure, similar to the one found in prokaryotic gene regulatory proteins [3]. Since animals, plants, and fungi possess homeobox genes, the origin of such genes preceded the divergence of these kingdoms [4]. Among these kingdoms, animal homeobox genes are the most diverse due to extensive gene duplication in the early eumetazoan lineage [5].
We previously identified the retina and anterior neural fold homeobox (Rax, also known as Rx) gene, which plays critical roles in the eye and forebrain development of vertebrate species [6][7][8]. Vertebrate Rax is composed of an N-terminal octapeptide, a paired-type homeobox, and a C-terminal OAR motif [6]. In the early mouse embryo, Rax is expressed in the anterior neural fold [6]. Subsequently, its expression is limited to the embryonic diencephalon region, which develops into the retina and pineal gland [6]. Rax-null mouse embryos do not form optic vesicles and exhibit the reduction of brain structures [8]. Likewise, mutations of the RAX gene were reported in human microphthalmia patients [9,10]. In the retina, Rax plays an essential role in cell fate determination and maturation of photoreceptor cells [11,12]. It has been shown that Pax6, another homeobox gene, plays an essential role in eye development [13]. It should be noted that, in Pax6-null mouse embryos, optic vesicles are formed and the Rax expression is unaffected, but cell proliferation in optic vesicles is severely impaired, resulting in a defective eye structure at later developmental stages. On the other hand, the cornea and lens are not formed in Pax6-null mouse embryos [14]. Thus, Rax is one of the critical transcription factors functioning at the initial stage of eye development, but acts independently of Pax6 [15,16].
As a result of recent advances in DNA sequencing and computation, whole-genome sequencing has become widely available [17]. To date, 2618 animal genomes including those of 1171 invertebrates have been sequenced, according to the NCBI Assembly database [18]. Since invertebrates diverged from vertebrates more than 500 million years ago [19], the genome sequences of invertebrates provide us with an unique opportunity to study the origin and evolution of genes [20]. Previous studies on the molecular evolution of Rax focused primarily on vertebrates [21] or on Bilateria, Cnidaria, and Placozoa [22,23]. This may be due to the fact that the number of genomic sequences available when these studies were conducted was very limited compared to those currently available. Therefore, to investigate the origin and molecular evolution of Rax and to gain insights into the evolution of the eye, we conducted a comprehensive evolutionary analysis of Rax. To do so, we analyzed the abundant number of currently available genome sequences, including Ctenophora and Porifera in addition to Bilateria, Cnidaria, and Placozoa.

Collection of Rax orthologs
To identify Rax orthologs, we downloaded NCBI Gnomon gene models of various species (https://www.ncbi.nlm.nih. gov/genome/annotation_euk/gnomon/). Gnomon gene models were constructed using comprehensive gene predictions with a combination of homology searching and ab initio modeling. For every species analyzed, we obtained protein-coding sequences from genome sequences based on the corresponding NCBI Gnomon gene models. We obtained complete protein sets by translating these protein-coding sequences. To identify putative Rax ortholog sequences, we performed blastp against every complete set of protein sequences using the Rax protein sequences for human (NP_038463.2), octopus (XP_014777656.1), and Pocillopora damicornis (XP_027036745.1) as query sequences with E-values < 1eÀ10. In cases where Rax was not identified in the complete set of protein sequences in a species, we performed tblastn against its genome sequence using the above three query sequences with E-values < 1eÀ10. All protein sequences for putative Rax orthologs were subjected to a blastp search against all human protein sequences to confirm their orthologous relationships with human RAX. To identify protein-coding sequences of Rax from transcriptomic data, we downloaded publicly available RNA-seq raw reads from the NCBI SRA database [24] and performed de novo transcriptome assembly using Trinity under default settings [25]. We searched for Rax putative protein-coding sequences in the Trinity contigs using tblastn as described above. The protein sequence of Meara stichopi Rax (AVK72338.1) [26] was obtained from the NCBI nucleotide database. In every Rax ortholog, regions of the octapeptide, homeodomain, and OAR motif were defined with reference to human RAX. The complete list of accession numbers for the taxon names, genome assemblies, and Rax orthologs is provided in Tables 1 and 2. Domain organizations of genes or proteins were illustrated by Illustrator for Biological Sequences [27].
Multiple sequence alignment of the octapeptide, homeodomain, or OAR motif in Rax orthologs Amino acid sequences of the octapeptide, homeodomain, or OAR motif in Rax orthologs were aligned by CLUSTAL OMEGA with the default parameters [28]. Resulting multiple sequence alignments were verified and visualized by JALVIEW [29].

Molecular phylogenetic analysis of Rax and Rax2 of jawed vertebrates and Rax of jawless vertebrates
Amino acid sequences of Rax and Rax2 of jawed vertebrates and Rax of jawless vertebrates were aligned using CLUSTAL OMEGA [28] and MUSCLE [30] under default parameters. The multiple sequence alignment results were verified and visualized using JALVIEW [29]. Maximum-likelihood trees were constructed using the Poisson, Whelan and Goldman (WAG), Le-Gascuel (LG), or Jones-Taylor-Thornton (JTT) models using MEGA7 [31]. Neighbor-joining trees were constructed with the Poisson, Dayhoff, or JTT models using MEGA7 [31]. All positions with < 90% site coverage were excluded from analyses. In other words, fewer than 10% alignment gaps or missing data were allowed at any position. The bootstrap values were estimated from 500 replicates in all analyses.

Synteny analysis of mammalian Rax and Rax2
Genome sequences and annotations were obtained from the NCBI Assembly database. In this database, the genome assembly quality is classified into four categories, in order of highest to lowest quality: complete genome, chromosome, scaffold, and contig (https://www.ncbi.nlm.nih.gov/ assembly/help/). We used genome assemblies of scaffold to complete genome quality in this analysis. The arrangements of genes around Rax or Rax2 were compared between species. Even if a relatively high-quality genome assembly is used for analysis, low-quality regions are often included to some extent due to low sequencing read coverage or the presence of repetitive sequences [32]. Therefore, regions with fewer than three genes surrounding Rax or Rax2 were excluded. We reported the genome analysis results where Rax and Rax2 loci were identified.

Maximum-likelihood tree construction based on mammalian Rax and Rax2 alignment
The amino acid sequences of 86 placental mammalian Rax, 75 placental mammalian Rax2, opossum Rax, and opossum Rax2 protein sequences were aligned using CLUSTAL OMEGA under default parameters [28]. Based on this alignment, a maximum-likelihood tree was constructed with the JTT model using MEGA7 [31]. All positions with < 90% site coverage were excluded from analyses. Bootstrap values were estimated from 500 replicates. The complete list of accession numbers for the analyzed protein sequences is provided in Table 2.
Calculation of nonsynonymous-to-synonymous substitution ratio The amino acid sequences of 86 placental mammalian Rax, 75 placental mammalian Rax2, opossum Rax, and opossum Rax2 protein sequences were aligned using CLUSTAL OMEGA under default parameters as described above [28]. Based on this alignment and the set of protein-coding sequences, we generated codon alignment using tranalign [33]. By comparing human RAX and RAX2 with respective mammalian Rax and Rax2 orthologs, we calculated nonsynonymousto-synonymous rate ratios (Ka/Ks) for each ortholog pair using the Jukes-Cantor model. All positions with < 90% site coverage in the alignment were excluded from analyses. The average Rax Ka/Ks and Rax2 Ka/Ks were compared using a Welch two-sample t-test. The difference was considered statistically significant if the P value was < 0.05.

Identification of Rax in various animal species
To investigate the evolutionary origin of Rax, we comprehensively searched for Rax in the genomes or transcriptomes of animals that are evolutionarily distant from each other. The criteria to determine whether a Rax ortholog is present in a species are described in Materials and Methods. This analysis included genome sequences of 34 animal species: two Porifera, three Ctenophora, two Placozoa, four Cnidaria, and 23 Bilateria (Fig. 1A, Table 1). Transcriptome data from Sycon ciliatum, a Porifera organism, and Mnemiopsis leidyi, a Ctenophora organism, were also analyzed. In all Cnidaria and Bilateria analyzed, we identified Rax orthologs (Fig. 1A). In contrast, we did not identify any Rax gene in Porifera, Ctenophore, and Placozoa, which are groups phylogenetically more distant from both Bilateria and Cnidaria (Fig. 1A).
Most of the Rax genes in Cnidaria and Bilateria were shown to have all of the octapeptide, homeodomain, and OAR motif (Fig. 1A). Sequence alignment analyses revealed that amino acid sequences of octapeptide, homeodomain, and OAR motif are highly conserved among these animals (Fig. 1B). These results suggest that Rax appeared in the common ancestor of Bilateria and Cnidaria, and has been highly conserved in terms of domain organization and sequence similarity over the course of evolution.
Phylogenetic analysis of Rax and Rax2 in jawed and jawless vertebrates Vertebrates are divided into two major groups, jawed and jawless, depending on whether the jaw is present. Jawed vertebrates possess Rax2 in addition to Rax [12,21]. The high sequence similarity of jawed vertebrate Rax and Rax2 suggests that they resulted from gene duplication. We analyzed the genomes of jawed and jawless vertebrate species to estimate the evolutionary timepoint when these two genes appeared. We analyzed the genomes of elephant shark, spotted gar, and coelacanth as representatives of jawed vertebrates.
On the other hand, as representative of jawless vertebrates, we analyzed the genomes of lamprey and hagfish, whose genomes were recently sequenced. In jawed vertebrates, we identified both Rax and Rax2 genes (Fig. 2). The arrangement of the genes Malt1-Rax-Cplx4 and their paralogous counterparts was conserved in these organisms. In contrast, we identified only single Rax in both lamprey and hagfish (Fig. 2). Notably, the arrangements of genes around Rax in lamprey or hagfish were very similar, suggesting that their Rax genes are orthologous to each other (Fig. 2). We next analyzed the phylogenetic relationships between jawless vertebrate Rax, jawed vertebrate Rax, and jawed vertebrate Rax2. Tetrapod Rax2 lacks the N-terminal region, including octapeptide, and is shorter than Rax [21]. Therefore, we focused on nontetrapod vertebrate Rax2 for molecular phylogenetic analysis in order to obtain as much phylogenetic information from the sequence alignments as possible. A total of 22 protein sequences were analyzed, including seven jawed vertebrate Rax, nine jawed vertebrate Rax2, two jawless vertebrate Rax, and four invertebrate Rax. To perform robust molecular phylogenetic analysis, we used the CLUSTAL OMEGA [28] and MUSCLE [30] programs to generate two multiple protein sequence alignments (Fig. 3). Based on these alignments, we constructed phylogenetic trees using the maximum-likelihood method in the character state methods and the neighbor-joining trees in the distance matrix methods (Fig. 4, Figs S1 and S2). Maximumlikelihood trees were constructed using the Poisson, WAG, LG, or JTT models. Neighbor-joining trees were constructed using the Poisson, Dayhoff, or JTT models. In all cases, lamprey and hagfish Rax formed  a sister group to Rax and Rax2 of jawed vertebrates (Fig. 4, Figs S1 and S2). Taken together, the current synteny analysis and molecular phylogenetic analysis suggest that Rax and Rax2 of jawed vertebrates resulted from segmental duplication of a small region containing Malt1, Rax, and Cplx4 ancestors that occurred after jawed vertebrates diverged from jawless ones.

Comparative analysis of Rax and Rax2 gene structures in vertebrates
Tetrapod Rax2 genes were reported to lack octapeptide domains [21]. To investigate how the loss of octapeptide in tetrapods occurred, we compared the gene structures of vertebrate Rax and Rax2. We included seven vertebrates from shark to human in this analysis (Fig. 5A). In all species analyzed, Rax or Rax2 gene was composed of three exons (Fig. 5A). In both genes, octapeptides were coded in the first exon (Fig. 5B). Start codons of Rax were located on the first exons in all species (Fig. 5A). Similarly, start codons of Rax2 in shark, spotted gar, and coelacanth were located on the first exon; however, in all tetrapods analyzed, start codons of Rax2 were shifted to the second exon, resulting in the loss of octapeptides (Fig. 5A).

Identification of Rax2 gene loss events in mammals
Since mice are known to lack the Rax2 gene [12], we investigated whether more Rax2 gene loss events have  occurred in mammals by comparative analysis of Rax and Rax2 loci in mammals. Mammals are phylogenetically divided into four major groups: Euarchontoglires, Laurasiatheria, Afrotheria, and Xenarthra (Fig. 6A). We examined both Rax and Rax2 loci in 86 mammalian genomes ( Table 2). While all 86 Rax loci contained Rax genes, 11 Rax2 loci lacked the Rax2 gene ( Table 2). Of the investigated Euarchontoglires, rock rabbit and six rodent species lack Rax2 (Fig. 6B, Table 2). Notably, three squirrel species possess Rax2 genes, suggesting that an ancestor of rodents and one of the rabbits independently lost Rax2 genes (Fig. 6B, Table 2). In Laurasiatheria, ferret, hedgehog, and common shrew lack Rax2 genes (Fig. 6C, Table 2). Recent studies on the Eulipotyphla phylogeny indicated that hedgehog and common shrew are the sister group to star-nosed mole [34,35]. Since star-nosed mole has the Rax2 gene, a single Rax2 gene loss event appears to have occurred in the common ancestor of hedgehog and common shrew. In Afrotheria, elephant lacks the Rax2 gene (Fig. 6D, Table 2). In Xenarthra, we analyzed the armadillo genome and identified the Rax2 gene. In summary, we detected five independent gene loss events of the Rax2 gene in mammals (Fig. 6A).

Molecular phylogenetic analysis of mammalian Rax and Rax2
In order to further analyze mammalian Rax and Rax2 evolution, we aligned all 86 Rax and 75 Rax2 protein sequences identified in the current study and constructed a maximum-likelihood tree (Fig. 7A, Table 2). As expected, Rax and Rax2 formed a monophyletic group in the tree (Fig. 7A). The Rax2 branch lengths appeared to be longer than the Rax lengths. Therefore, to quantitatively compare the degree of amino acid substitutions, we compared the nucleotide substitutions between human RAX and RAX2 with their respective mammalian Rax and Rax2 orthologs. Then, we calculated Ka/Ks ratios for each ortholog gene pair. The Rax2 Ka/Ks values showed a broader distribution compared to Rax (Fig. 7B). The average Ka/Ks value was 0.042 for Rax and 0.070 for Rax2 (Fig. 7B), indicating that the average mammalian Rax2 Ka/Ks value was~67% greater than mammalian Rax (P < 0.01, Welch two-sample t-test; Fig. 7B).

Discussion
Our comprehensive analysis of Rax orthologs suggests that Rax appeared after Bilateria and Cnidaria   [28]. (B) Multiple sequence alignment of Rax orthologs using MUSCLE. The same set of protein sequences in (A) were aligned by MUSCLE [30]. Each residue is colored according to the Clustal X residue code [58]. diverged from other lineages over the course of evolution (Fig. 1A). It has remained unknown whether Rax is present in species evolutionarily distant from Bilateria and Cnidaria, probably because genome sequences of such distant species remained unavailable [23]. Fortunately, genome sequences of such distant species have recently become available, including Porifera, Ctenophora, and Placozoa, providing us with a valuable resource for comparative genomics [20]. Consistent with the previous studies, we definitively showed that Cnidaria and Bilateria possess Rax, whereas Placozoa does not (Fig. 1A) [22,23]. Conversely, we showed that Porifera and Ctenophora may lack Rax using a comprehensive analysis of their genomes or transcriptomes (Fig. 1A, Table 1). It has been proposed that the Hox genes diversified due to rapid gene duplication before diversification of Cnidaria and Bilateria [36]. Similarly, ancestral paired-type homeobox genes may have diverged, resulting in the appearance of the Rax gene before the diversification of Cnidaria and Bilateria. However, the divergence between Placozoa and the common ancestor of Cnidaria and Bilateria is very ancient. Therefore, our analysis cannot exclude the possibility that highly accumulated substitutions affect our Rax ortholog search results. The incompleteness of the genome assemblies should also be considered because all genome assemblies for Porifera, Ctenophora, and Placozoa are assembled at the contig or scaffold level. We also showed that the domain organization and amino acid sequences of the octapeptide, homeodomain, and OAR motif are highly conserved between cnidarian Rax and bilaterian Rax (Fig. 1B). Based on these observations, we propose that the origin of the Rax gene dates back to the common ancestor of Cnidaria and Bilateria and that Rax is highly conserved among Cnidaria and Bilateria.
From the very simple structure seen in Porifera to more complex structures, animal body plans have become more elaborate over the course of evolution [37]. Cnidaria were the first animal organisms to develop nervous systems [38]. Moreover, some Cnidaria in the medusozoan group display complex lens-containing eyes [39,40]. Since the current analysis suggests that Rax appeared in the common ancestor of Cnidaria and Bilateria, the evolutionary appearance of Rax might Pax6 is a paired-type homeobox gene [13], which is an ortholog of eyeless in flies and plays a critical role in eye formation in both flies and mammals. However, its evolutionary origin is after the divergence of Bilateria and Cnidaria [41,42]. Although the cnidarian PaxB gene is considered to be related to Pax6 in Bilateria, the domain organization and DNA-binding specificity of the paired domain differ between these two genes [41,42]. In contrast, cnidarian Rax has the same domain organization as bilaterian Rax. Furthermore, amino acid sequences of the octapeptide, homeodomain, and OAR motif are highly conserved between cnidarian Rax and bilaterian Rax (Fig. 1B). Based on these observations, we propose the following scenario for the roles of Rax and Pax6 in eye evolution: Rax appeared in the common ancestor of Bilateria and Cnidaria, predating Pax6 in terms of the evolutionary origin and the involvement in eye formation; after the emergence of Pax6 in Bilateria, Rax and Pax6 began to act jointly in the eye development of Bilateria. Future evolutionary analyses of other homeobox transcription factors involved in eye formation, including Six3, Six6, and Lhx2, may deepen our understanding of the evolution of the eye [15].
The previous study examining Rax evolution analyzed earlier versions of the lamprey genome assemblies [43,44] and identified one Rax gene [21]. They suggested that future studies may identify another Rax gene because of the incomplete nature of these genome assemblies [21]. The current study analyzed the latest assembly of the lamprey [45] and hagfish (GCA_ 900186335.2) genomes and identified one Rax gene in both genomes (Table 1). Moreover, our synteny analysis results suggest that the lamprey and hagfish Rax loci are orthologous (Fig. 2). Taken together, the current results further support the possibility that jawless vertebrates only possess one Rax.
Based on the results of our synteny and molecular phylogenetic analyses, we propose an alternative origin hypothesis of Rax and Rax2 in jawed vertebrates. These two genes might have resulted from segmental duplication of a small region containing Malt1, Rax, and Cplx4 ancestor genes in the common ancestor of jawed vertebrates (Fig. S3). This conclusion conflicts with the previous hypothesis that vertebrate Rax and Rax2 resulted from two rounds of whole-genome duplication (WGD) [21]. Following two rounds of WGD that occurred at the root of vertebrates, many vertebrate genes have two to four paralogs [46]. For example, vertebrate genomes contain four Hox gene clusters or three Otx family genes: Otx2, Crx, and Otx5 [47]. Likewise, the previous study used molecular phylogenetic and synteny analyses to conclude that vertebrate Rax and Rax2 originated from two rounds of WGD that occurred in the common ancestor of vertebrates [21]. The authors conducted phylogenetic analysis including jawed vertebrate Rax, jawed vertebrate Rax2, and lamprey Rax. However, they did not include invertebrate Rax as an outgroup. Therefore, lamprey Rax can be arbitrarily assigned to Rax or Rax2. The authors assigned the lamprey Rax to Rax2 without detailing their justification [21]. Further, synteny analysis showed that the Rax and Rax2 loci were mapped to the same regions of the lancelet genome [21]. The authors used their synteny analysis results to support the conclusion that Rax and Rax2 originated from WGDs. However, segmental duplication of the ancient Rax locus could produce similar synteny analysis results (Fig. S4). Segmental duplications in vertebrate genomes are commonly observed. For example, 4% of the human genome is covered by duplications, with segmental duplication accounting for up to 14% in individual chromosomes [48]. Segmental duplication is believed to occur via nonallelic homologous recombination in regions flanked by highly homologous sequences [49]. Since it is very likely that the genomes of jawed and jawless vertebrates' common ancestor contained highly homologous duplicated sequences, such as transposable elements, segmental duplication events could occur frequently in their genome. Together, these considerations indicate that the synteny analysis results alone cannot completely exclude the possibility of segmental duplication. Moreover, we included four invertebrate Rax sequences as outgroups and used the lamprey and hagfish Rax sequences from their latest genomes [45] to perform more robust phylogenetic analyses than the previous study [21]. The current molecular phylogenetic analysis indicated that lamprey and hagfish Rax forms a sister group with Rax and Rax2 in jawed vertebrates, indicating that jawed vertebrate Rax and Rax2 originated from lineage-specific segmental duplication events, not the WGDs (Fig. 4, Figs S1 and S2). However, since it is known that jawless vertebrates show amino acid composition biases, resolving orthology among jawless vertebrate Rax and jawed vertebrate Rax and Rax2 is challenging [50]. Therefore, it should be noted that our phylogenetic analysis results cannot exclude the possibility that Rax and Rax2 generation in jawed and jawless vertebrates is due to the two rounds of WGD as proposed in the previous study [21].
Another possible explanation for the current molecular phylogenetic analysis results regarding Rax and Rax2 of jawed vertebrates and Rax of jawless vertebrates is a delayed rediploidization after genome duplication [51]. In this model, following WGD, speciation predates rediploidization [51]. This leads to independent ohnolog divergence in sister lineages that share a common WGD event and provides ohnologs solely available for lineage-specific adaptation [51]. It has been reported that 27.1% of ohnologs showed delayed rediploidization in salmonid fish [51]. Resolving orthology is difficult if ohnologs of interest independently diverged in sister lineages that share a common WGD. Therefore, it should be noted that the current molecular phylogenetic analysis results can also be affected by delayed rediploidization.
A comprehensive ortholog search for Rax and Rax2 in 86 mammalian genomes from all four major mammal groups found at least five independent Rax2 gene loss events (Fig. 6). These comprehensive analyses enabled us to raise an alternative explanation regarding the Rax2 loss in lagomorph and rodent (Glires). The previous study proposed that Rax2 was lost in a common ancestor of lagomorph and rodent [21]. However, they did not show the presence of Rax2 in squirrel species, which are a sister group to other rodent species [21]. In contrast, the current study demonstrated that Rax2 is present in the thirteen-lined ground squirrel, arctic ground squirrel, and yellow-bellied marmot (Fig. 6B). This finding suggests that Lagomorpha and Rodent independently lost Rax2.
We observed a loss of the Rax2 octapeptide in tetrapods and five independent Rax2 gene loss events in mammals (Figs 5 and 6). In contrast, no Rax gene loss events were identified in the analyzed mammalian genomes, suggesting that Rax is a highly evolutionarily conserved and functionally significant gene in mammals. Rax gene loss events may not be present in the analyzed mammalian species because it plays an essential role in central nervous system development [8]. Deletion of the Rax gene in mice, which lack the Rax2 gene, results in severe brain malformation, such as the absence of the ventral forebrain and failure of the optic vesicle to form [8]. Conversely, Rax can functionally compensate for loss of mammalian Rax2 in mice [6][7]11,12]. In humans, unlike RAX2, RAX mutations are associated with symptoms affecting the whole eye. RAX mutations result in microphthalmia [9,10], whereas RAX2 mutations are associated with cone-rod dystrophy or age-related macular degeneration [52,53]. Since RAX2 mutations can lead to age-related disease, we hypothesize that the effects of RAX2 loss in some mammal lineages occur after the age of sexual maturity. Therefore, RAX2 loss has little effect on fitness. However, it also should be noted that sudden RAX2 loss cannot be compensated by RAX, as indicated by the association of RAX2 mutations with human diseases [52,53]. Evolutionary deletion of Rax2 from mammal genomes might require gradual accumulation of amino acid substitutions. We found that the average Ka/Ks ratio of mammalian Rax2 was~67% greater than that of mammalian Rax (Fig. 7B). This difference between mammalian Rax and Rax2 might partially explain why Rax2 is more defect-prone than Rax in this animal group.

Supporting information
Additional supporting information may be found online in the Supporting Information section at the end of the article. Fig. S1. Maximum-likelihood trees of Rax and Rax2 in various animal species (related to Fig. 4). Fig. S2. Neighbor-joining trees of Rax and Rax2 in various animal species (related to Fig. 4).