Pattern of Gene Duplications and Gene Conversion

Sixty three pairs of two-copy duplicated genes with synonymous divergence K_S<0.2 were identified in the D. melanogaster genome (see Methods). This K_S cutoff value was chosen such that almost all duplicated genes in the D. melanogaster genome that appeared after the speciation of D. melanogaster and D. simulans can be detected. Note that the average K_S between the two species is around 0.12 [21], so that the probability that K_S between duplicates exceeds 0.2 should be very low. Then, the locations of these genes on the D. melanogaster genomic sequence were visually examined, and by using the BLASTN algorithm we identified duplicated genomic regions (blocks) that encompass the identified duplicated genes. It was found that the 63 duplicated genes belong to 55 duplication blocks: some of them are next to each other and belong to the same duplication blocks (summarized in Tables 1 and 2). Almost all duplicates are located on the same chromosomes. For each pair of the duplicated blocks, the one that is close to the telomere of the left arm of the chromosome was assigned to Xm and the other was assigned to Ym. These results are consistent with those of Fiston-Lavier et al. [27].

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Table 1. Summary of the Post-speciation Duplicated Blocks.

https://doi.org/10.1371/journal.pgen.1000305.t001

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Table 2. Summary of the Pre-Speciation Duplicated Blocks.

https://doi.org/10.1371/journal.pgen.1000305.t002

We identified the orthologous regions of these duplicated blocks in the D. simulans and D. sechellia genomes, and the results are shown in Tables 1 and 2. For the 25 blocks in Table 1, there is only one orthologous region, while the orthologous regions of both the duplicated blocks are found in the D. simulans and/or D. sechellia genomes for the remaining 30 blocks (Table 2). The orthologs of Xm and Ym are denoted by Xs and Ys, respectively, in Table 2. The locations for Xs and Ys are those in the D. simulans genome if Xs and Ys are found in this species, otherwise the locations are those in the D. sechellia genome. The relative chromosomal locations and orientations of the blocks in the two species are consistent with each other for most of the duplicated blocks. Considering that it is very unlikely that the identical size of duplication occurred at the same genomic location and in the same orientation independently on the lineages leading to D. melanogaster and D. simulans (D. sechellia), it may be reasonable to consider that the duplicates in Table 2 were created by a single duplication event before the speciation of the two species. Therefore, these duplicates are referred to as “pre-speciation duplicates”. Note that the difference in orientation for Pre12 can be explained by a large inversion difference on chromosome 3R [28]. Pre5 and Pre11 are only exceptions, for which the possibilities of independent duplications cannot be ruled out although single duplication plus inversion will also explain them. In the following analysis, we treat all duplicated blocks in Table 2 as pre-speciation duplicates, but exclusion of Pre5 and Pre11 has very little effect on our conclusions. The duplicates in Table 1 are called “post-speciation duplicates” because they likely arose after the speciation of D. melanogaster and D. simulans.

For all post- and pre-speciation blocks, NJ trees on the basis of nucleotide divergence are constructed with D. yakuba homologs as an outgroup (Figure S1 and S2). The phylogenetic relationship is relatively simple for the post-speciation blocks (Figure S1): D. melanogaster has two copies while D. simulans and D. sechellia have one copy each, suggesting that the duplication events occurred after the speciation of D. melanogaster and the other two species. For the pre-speciation duplicated blocks, in most cases, phylogeny includes two duplicates in D. melanogaster and their orthologs in D. simulans and D. sechellia (Figure S2).

Figure 2 shows the distributions of K_S for the two classes of duplicated blocks. The overall distribution is L-shaped as reported by Lynch and Conery [13], mainly due to the excess of duplicated blocks with low K_S. Almost all post-speciation blocks have K_S<0.1 except for Post25. The tree for Post25 in Figure S1 shows that the duplicates in D. melanogaster are most closely related each other. It seems that the divergence is high only in synonymous sites in the coding region.

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Figure 2. The distribution of synonymous divergence between duplicated blocks in D. melanogaster.

K̅_S is the average synonymous divergence for blocks with multiple coding genes. Post-Sp. and Pre-Sp. mean duplicates that arose after and before the speciation event of D. melanogaster and D. simulans, respectively.

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K_S for the pre-speciation blocks are also low. If the two duplicated blocks have accumulated substitutions independently (i.e., a molecular clock holds for the paralogous divergence), the expectation of K_S for the pre-speciation blocks is larger than K_Sspecies, which is the orthologous divergence at synonymous sites. The genome-wide average of K_Sspecies is 0.12 [21]. Although there should be variation in K_Sspecies across genes, our observation is quite unlikely under a molecular clock model, indirectly suggesting that those duplicated genes are undergoing concerted evolution by gene conversion.

The role of gene conversion can be directly and clearly documented by examining the shape of the gene tree of the duplicated genes. If the duplicated blocks X and Y in the two species are currently undergoing concerted evolution, the two paralogous regions in each species are more closely related than the orthologous pairs, as illustrated in Figure 1C. Without gene conversion, the orthologous pairs should be more closely related (Figure 1B). It is also possible that only one paralogous pair is undergoing concerted evolution while the other is not (Figure 1D). Based on this idea, we investigated the shapes of the trees in Figure S2, which is summarized in Table 3. Out of the 28 blocks to which the analysis can be applied (excluding two blocks with no outgroup sequence available), 14 exhibited evidence for gene conversion for both species (i.e., the tree shape in Figure 1C), and evidence for gene conversion is obtained for either of the two species (i.e., Figure 1D) for 10 blocks. It seems that the effect of gene conversion in D. simulans and D. sechellia is not as extensive as that in D. melanogaster, because nine of the 10 blocks have the Xm-Ym cluster (Table 3). However, this can be simply explained by the ascertainment bias of our sampling of duplicates: our sample is biased toward those with low paralogous divergence in D. melanogaster. No evidence for gene conversion is obtained in four blocks.

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Table 3. Testing for Gene Conversion in the Post-Speciation Duplicated Blocks.

https://doi.org/10.1371/journal.pgen.1000305.t003

The power to detect evidence for gene conversion should increase if we perform a window-analysis of the tree shape. This is because the tree shapes in Figure S2 (also summarized in Table 3) reflect the average evolutionary relationship over the entire region (block). Therefore, this approach could potentially miss signatures of gene conversion when occurring only in local regions. In other words, the approach can detect evidence for gene conversion when it frequently occurs in most of the analyzed region. The results of the window analysis are also shown in Figure S2, where regions with red bar have tree shapes illustrated in Figure 1C (evidence for gene conversion in both species), while regions with blue bar have tree shapes illustrated in Figure 1B (no evidence for gene conversion). We observe that the tree shape changes across duplicated regions, indicating that different regions have different evolutionary histories. This is expected because gene conversion tracts should be much smaller than the duplicated regions. It is also suggested that there could be substantial local variation in the activity of gene conversion. Overall, there is evidence for extensive gene conversion. We found that in most of the analyzed blocks, the regions of red bar (i.e., supporting the tree shape of Figure 1C) distribute along the entire region. All blocks investigated have at least one local region (window) supporting the tree shape of Figure 1C.

A drawback of this analysis is that the relative effect of other noises, including multiple mutations, would be large because phylogeny is constructed for short regions (windows). In other words, a small number of sites with multiple mutations could mimic the real evolutionary history of the duplicated blocks. Therefore, we apply a statistical test that incorporates the effect of multiple mutations. The null hypothesis is set such that the evolutionary history in the entire duplicated region follows the tree shape of Figure 1C, so that the observation could be explained without gene conversion when the effect of multiple mutations is taken into account. The P-value is the rejection probability of this null hypothesis; therefore, a smaller P-value indicates a stronger evidence for gene conversion.

The statistical analysis is based on the alignment of the four sequences, Xm, Ym, Xs, and Ys (Figure 3). We focus on two types of informative sites in the alignment, denoted by type-C and type-N sites (Figure 3A). The former is a biallelic site at which the same nucleotide is shared by the two paralogous sequences in each species, while the latter is that at which the same nucleotide is shared by the two orthologous sequences (Figure 3A). A type-C site parsimoniously supports a tree with gene conversion (i.e., the left tree in Figure 3B), while a type-N site supports a tree with no gene conversion (i.e., the right tree in Figure 3B). Let j and k be the observed numbers of type-N and type-C sites, respectively. The presence of type-C sites (k>1) parsimoniously suggests that (at least a part of) the duplicated block experienced gene conversion, but multiple mutations could also explain it, especially when k≪j. The statistical test examines if the observed number (k) can be explained by multiple mutations assuming no gene conversion (see Methods). As shown in Table 3, the P-value is less than 0.05 for almost all pre-speciation blocks (29/30), most of which exhibit very strong evidence with P<0.0001. The exception is Pre19 for which only one informative site is available; thus, almost no statistical power is expected.

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Figure 3. Illustrations to describe the analysis of informative sites in the alignment of the four sequences.

(A) Example of the alignment of the four sequences. The types of informative sites are shown below the alignment: “C” and “N” are as defined in the text, and “M” represents a site that requires multiple mutations for explanation. (B) Relationships of the four sequences at type-C and type-N sites. (C) Patterns of double mutations. A double-mutated site is defined as one with a single substitution that has occurred since the speciation event in each of X and Y.

https://doi.org/10.1371/journal.pgen.1000305.g003

Rate of Gene Duplication

We use our list of 1→2 duplications to estimate the rate of gene duplication. Note that our interest is in the long-term duplication rate, that is, the rate at which a duplicate arises by mutation and becomes fixed in the population. As mentioned in the Introduction, our focus is limited to two-copy duplicates to perform the fine-scale analysis at the DNA level. Therefore, the rate we estimate can be considered to be the rate at which a single-copy gene becomes two-copy duplicated genes. In this sense, the rate we are interested in is quantitatively different from those estimated in other articles [13],[22].

We have identified 63 gene duplications by which single-copy genes became two-copy genes. It was found that 31 of them are in the 25 post-speciation blocks, indicating that these 1→2 duplications occurred after the speciation of D. melanogaster and D. simulans, which was roughly 2.3 million years ago [29]. It can be estimated that a 1→2 duplication occurs every 0.074 million years, or the duplication rate per gene is 1.0×10⁻⁹, given that there are about 13,000 single-copy genes in the genome.

The advantage of this phylogeny-based method is that it is robust to the effect of gene conversion, which could cause a serious overestimation of gene duplication rate when estimated by counting duplicated genes with low divergence [15]. To investigate this effect of gene conversion, we estimated the 1→2 duplication rate following the method of Lynch and Conery [13]. We found 25 two-copy duplicated genes with synonymous divergence K_S<0.01. Their ages should be smaller than 2.3×10⁶×0.01/0.12 = 1.9×10⁵ years. Thus, the divergence-based method produced the duplication rate per gene as 10.0×10⁻⁹, which was roughly 10 times larger than our estimate.

Decay of Duplication Blocks

Figure 4 displays the evolutionary changes in the size of duplicated blocks, the number of genes in each block, and the length of the intervening sequence between each pair. To understand their evolution over time, we used two methods to measure time. The first is the paralogous synonymous divergence (K_S). Although K_S is not a very good measure because of gene conversion (see above), theory predicts that K_S at least shows a positive correlation with time since the duplication event [15]. Second, we directly compared the two classes of duplicates for the three characteristics of interest.

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Figure 4. Decay of duplicated blocks.

(A) Length of duplicated blocks (L) vs. synonymous divergence (K_S). (B) Number of annotated genes vs. K_S. (C) Length of intervening region (I) vs. K_S.

https://doi.org/10.1371/journal.pgen.1000305.g004

The relationship between K_S and the block size is shown in Figure 4A. The sizes of duplicated blocks with K_S<0.01 ranges from 1 kb to 35 kb, while the size is generally smaller than 2 kb for those with K_S>0.1. K_S and the block size show a strong negative correlation, and Pearson's correlation coefficient is r = −0.288, which is highly significant (p<0.0001, permutation test). It is also found that the average block size of the post-speciation blocks is significantly larger than that of the pre-speciation blocks (p = 0.0012, permutation test), indicating that young blocks are likely to be large.

Additionally, the number of genes (denoted by s_X and s_Y in Tables 1 and 2) in a block also decreases with increasing K_S (r = −0.396, p<0.0001, permutation test). The average number of genes in the post-speciation blocks is significantly larger than that of the pre-speciation blocks (p = 0.0124, permutation test). It seems that young duplicated blocks have more genes. We found unannotated pseudogenes in several blocks, which resulted in s_X≠s_Y in Tables 1 and 2, suggesting that pseudogenization of redundant duplicated copies is underway. We also found that some orthlogs in D. simulans and/or D. sechellia have frameshift mutations (see Table 2).

Insertion/deletion is the mechanism to affect the size of duplicated blocks. Petrov et al. [30] reported that the deletion rate may be higher than the insertion rate in retrotransposons in the D. melanogaster genome. If this can be applied to duplicated regions, the biased pressure toward deletion would partly explain the observed decay of the sizes of duplicated blocks. The decay of the sizes of blocks could also be simply explained by technical limitations to identify the real duplicated regions. It may be easy to imagine that the accumulation of nucleotide mutations and small insertion/deletions around the edges of the duplicated regions could result in misidentification of the duplicated regions; usually, the “identifiable” region is smaller than the real region.

We propose that the decay of “identifiable” duplicated blocks can be enhanced by the combination of two opposing forces, mutation (including small indels) and gene conversion. Obviously, the former increases the divergence between duplicates, the latter decreases the divergence, and their balance determines the divergence between paralogs [31],[32],[33]. It may be reasonable to assume that the spatial distribution of the mutation rate would be roughly uniform, but there could be a substantial amount of local variation in the gene conversion rate. Because interlocus gene conversion is a kind of recombination event [2], we expect that the rate of paralogous synapses may be lower around the edges due to decreased sequence identity. As a consequence, the rate of gene conversion would be low around the edges. The divergence in these regions possibly increases more rapidly in comparison with that in regions far from the edges. This contrast in the pressure of homogenization by gene conversion could result in the misidentification of duplicated regions.

This process predicts two outcomes. (i) The length of the intervening sequence between “identifiable” duplicated blocks (denoted by I) increases over time. This can be well documented if all duplication occur tandemly with no intervening region (i.e., I = 0), but this is not the case in practice. Nevertheless, the prediction of increased intervening sequences may still be supported because all duplicated blocks with I = 0 are in the post-speciation class, and almost all (10/11) duplicated blocks with I = 0 have K_S<0.01 (Tables 1 and 2). However, because many other mutational mechanisms are involved in the length evolution of intervening sequences, the relative contribution of the decay of duplicated block to the growth of intervening sequences may not be large. (ii) The second outcome would be seen in the distribution of the nucleotide divergence between duplicated blocks. The decay of the identifiable duplicated blocks could be visualized if the divergence is elevated around the edges when a high level of identity is observed in the middle of the block. Figure S2 illustrates the distribution of the paralogous divergence (blue line), which shows that many pre-speciation duplicated blocks have elevated divergence around the edges. Two examples with very clear patterns are picked up and shown in Figure 5. The first example is Pre6, which encompasses the Bob (Brother of Bearded) genes, and the second is Pre16 with the Amy (amylase) genes. In both, the divergence between paralogs is high around the edges of the identified blocks. Because the spatial distribution of orthologous divergence between the two species is not necessarily U-shaped in both the cases, the relaxation of negative selection outside the coding regions alone cannot explain the observation. The latter case is a typical example of duplicated genes with strong evidence for long-term concerted evolution by gene conversion [34],[33]. The two duplicates are shared by the D. melanogaster subgroup, indicating that the duplication occurred at least ∼10 million years ago. Such a long-term concerted evolution was achieved by frequent gene conversion: the rate has been estimated to be roughly 100 times higher than the synonymous mutation rate [32],[33],[35].

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Figure 5. Distributions of the divergence between duplicated blocks, obtained by a window analysis with size 100 bp.

(A) Pre6 block with the Bob genes. (B) Pre16 with the Amy genes.

https://doi.org/10.1371/journal.pgen.1000305.g005

Thus, we have demonstrated that the size of “identifiable” duplicated blocks will shrink over time together, which can be explained by the accumulation of point mutations and ineffective gene conversion around the edges. The upshot is that it is difficult to know the real sizes of old duplicated blocks.

Evolutionary Rate after Duplication

An acceleration in amino acid-changing substitutions (K_A) after gene duplication is usually considered as a signature of neofunctionalization, although the relaxation of negative selection could also elevate the rate of non-synonymous substitutions. As shown in Tables 1 and 2, K_A is smaller than K_S in most cases, indicating the operation of purifying selection. Although several blocks have K_A>K_S, the ratio K_A/K_S is not significantly higher than 1.

Asymmetry of the evolutionary rate after gene duplication is another signature of neofunctionalization. Our data provide an opportunity to investigate the rate of molecular evolution in the original vs. derived copies. Since Ohno proposed his model of evolution of genetic novelty by gene duplication [1], this hypothesis has been challenged by many researchers [36],[37],[38]. Ohno's neofunctionalization model describes the process such that after a duplication, as long as one copy maintains the original function, the other is completely free from purifying selection. Therefore, Ohno's prediction has been tested for many species by looking at the symmetry (or asymmetry) of the evolutionary rate after gene duplication. However, those analyses did not specify which duplicates are original and which are derived copies. Here, with the availability of the genome sequences of D. simulans and D. sechellia, we were able to confidently define duplicates as original or derived copies for six of the post-speciation blocks (see Methods). We performed a relative rate test [39] by using the MEGA 3.1 program package [40] for genes in those six blocks, but we did not observe any significant trend in the acceleration of substitutions in the lineages of the original and derived copies.

Signature of Selection for Neofunctionalization under the Pressure of Gene Conversion

Teshima and Innan [24] recently proposed a new test for detecting signature of neofunctionalization. Using this simple non-parametric test, we performed a genome scan for recent neofunctionalization in D. melanogaster. The test can be best applied to relatively old duplicated blocks that are currently undergoing concerted evolution. In our data, the pre-speciation blocks with strong evidence for gene conversion should be suitable for this analysis. Because a simple search for locally diverged regions may capture false positives created in regions of less functional importance, we focused on the distributions of type-C and type-N sites. A cluster of type-N sites would be considered as a signature of neofunctionalization, which can be emphasized when there are many type-C sites in the surrounding regions of the cluster. A simple sliding-window analysis (see Methods) found such a pattern in one of the pre-speciation blocks. Figure 6 shows the distributions of type-C and type-N sites in Pre28 (below and above the horizontal axis, respectively). The observation is very well-consistent with the theoretical expectation with selection. There are two clusters of type-N sites, which are surrounded by regions with abundant type-C sites. A forward simulation (see Methods) showed that the probability that a peak of divergence with >15% appears in a 1600 bp region is very low (P<0.0001), suggesting that selection may be working at the two locations.

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Figure 6. Distributions of divergences and type-C and type-N sites in Pre28, including the CG18281-CG17637 gene pairs in D. melanogaster.

The orthologous divergence (d₀) is the average of d_Xm−Xs and d_Ym−Ys.

https://doi.org/10.1371/journal.pgen.1000305.g006

The two clusters are located in the coding regions of CG18281 (region X) and CG17637 (region Y), which belong to the major facilitator superfamily. The members in the major facilitator superfamily transport small solutes such as sugar and drugs in response to chemiosmotic ion gradients [41]. These two genes have conserved homologs among many metazoan organisms. A BLAST-based conserved domain search (CD search) showed that these two proteins contain arabinose or drug efflux domains of bacteria in their N-terminal regions [42].

Figure 6 also shows the distributions of the paralogous divergences for the two species. As expected, two peaks of divergence are observed at the same locations in both the distributions. The red line in Figure 6 is the distribution of d_o, the divergence between the orthologous pairs, which is roughly flat across the region, indicating that the peaks of divergence are not due to the relaxation of purifying selection. This is also supported by an excess of non-synonymous type-N sites especially for the first peak around position 800 (14/20), indicating that the amino acid differences between duplicates may be preferred by selection. The distributions of the paralogous divergences for the two species are nearly identical, indicating that the peaks have been maintained by selection at least since the speciation of the two species.

This is also well-supported by phylogenetic trees in Figure S3. In the regions excluding the two peaks, the two paralogs in D. melanogaster are closely related to each other (Figure S3C). In contract, the tree for the first peak is consistent with the species tree (Figure S3A). The branch lengths in the tree in Figure S3A are overall longer than those in Figure S3B, suggesting an accelerated evolutionary rate in the region around the first peak. A similar pattern is also observed for the second peak, although the resolution of the tree is not very clear because the region is short (Figure S3B).

Gene Duplication and Gene Conversion

The pattern of recent 1→2 gene duplications in the D. melanogaster genome was investigated with special attention to interlocus gene conversion. Our fine-scale analysis with careful visual inspections enabled accurate identification of duplicated blocks. The orthologous parts of those duplicated blocks were also identified in the D. simulans and D. sechellia genomes, by which we were able to clearly classify most blocks into post- and pre-speciation duplicated blocks. Our analysis demonstrated that a number of duplicated blocks undergo concerted evolution by gene conversion. Almost all pre-speciation duplicated blocks exhibited strong signatures of gene conversion (Table 3, Figure S2).

Gene conversion and unequal crossingover are usually considered the major mechanisms of concerted evolution. In this study, we focused only on gene conversion because unequal crossingover is not relevant. Our fine-scale identification of recent duplicated blocks showed that the synteny around the duplicated blocks are very well-conserved among D. melanogaster, D. simulans and D. sechellia, indicating that there is no evidence of unequal crossingover.

The decay of duplicated blocks over time was observed. We found that (1) the length of duplicated blocks is large for young duplicates (post-speciation blocks), (2) young duplicated blocks include more genes, (3) all duplicated blocks with no intervening sequences (I = 0) belong to the post-speciation class. In addition to biased deletion rate, which may be possible for D. melanogaster [30], we postulate that the degeneration of gene conversion around the edges enhances the divergence between duplicates, causing the misidentification of the real duplicated region; usually, the “identifiable” region is smaller than the real region. Our hypothesis is supported by the elevated paralogous divergence around the edges of duplicated regions as shown in Figures 5 and S2.

Thus, we provided several lines of evidence that gene conversion plays a crucial role after gene duplication in the D. melanogaster genome. Although most of the duplicated blocks analyzed in this study were located close together on the same chromosome, interlocus gene conversion can occur between different chromosomes. By looking at the polymorphism data in a pair of duplicated genes located on chromosomes 3 and X, Arguello et al. [43] showed clear evidence that the pair has been undergoing long-term concerted evolution by gene conversion. Polymorphism data analysis is much more powerful to detect interlocus gene conversion, and there are a number of duplicated gene pairs with strong signatures of recent gene conversion in D. melanogaster [33],[35]. It seems that interlocus gene conversion is a genome-wide phenomenon. Therefore, its effect should be taken in account in any kind of evolutionary analysis of gene duplication.

Rate of Gene Duplication

We estimated the 1→2 gene duplication rate to be 1.0×10⁻⁹ per gene per year by using a phylogeny-based method. The method is robust to the effect of gene conversion, which is a great advantage. In contrast, a divergence-based method [13], which uses information from only a single genome, is very sensitive to gene conversion because it reduces the divergence between duplicated genes. We found that the divergence-based method provides an estimate of gene duplication rate about 10 times higher than that provided by the phylogeny-based method. The degree of overestimation is not as serious as in yeast, for which overestimation by the divergence-based method is about two orders of magnitude [11]. It should be note that the original estimate of Lynch and Conery is 2.3×10⁻⁹ per gene per year, which is only twice higher than ours even when they included small multigene families with sizes up to five. The reason for this is that they found only 10 duplicated gene pairs with K_S<0.01 probably because of the incompleteness of the D. melanogaster genome at the time.

This study focuses only on 1→2 duplications because our primary purpose was to perform a fine-scale analysis at the DNA level including non-coding regions, which has not been done in previous large-scale analysis in Drosophila [21],[22]. In this sense, this study is different from others, including that of [13],[22], and [21], who analyzed gene families with various sizes. The rates of duplication (as defined above) depend on the size of the multigene family. The duplication rate of single-copy genes (i.e., 1→2 duplication rate) should be lower than the rates of larger families (e.g., 2→3, 3→4,… duplication rates), when selection is working on copy number. For example, if over-expression by a duplicated extra copy is deleterious, the extra copy is subject to negative selection, and this selective pressure is stronger for single-copy genes [44]. Although Hahn et al. [22] reported lineage-specic expansion of gene families, we did not observe such expansion in our data, indicating that the copy-number evolution in small families is more stable than that in large ones. Nevertheless, the estimate of Hahn et al. [22] is 1.0×10⁻⁹ per gene per year, which is quantitatively consistent with ours. This is because their estimate is based on net copy size changes over a long evolutionary time, so that it does not reflect some duplications canceled out by losses. Our estimate (1.0×10⁻⁹ per gene per year) is quantitatively more consistent with an estimated rate of new gene formation through DNA-level duplication by Yang et al. [45]. Their estimate (0.12×10⁻⁹) is several times lower than ours because they ignore tandem duplications. They found that most of those events are 1→2 duplications. It may be possible to extend our analysis to a larger gene family although technically more difficult [46], but description of such an analysis is beyond the scope of this article.

Note that we define the duplication rate as the rate at which a single-copy gene is duplicated and fixed in the population. Although our estimates assumed that all identified duplicated blocks are fixed in the D. melanogaster population, it is possible that some of them are still polymorphic (i.e., copy-number polymorphism). If so, our estimates would be overestimated. If we exclude duplicates with too low K_S (say, K_S<0.01), our estimate turns out to be 0.4×10⁻⁹ per year, which can be considered as the lower limit of our estimate because this treatment might be too drastic: all duplicates with K_S<0.01 are considered to be polymorphic. Indeed, only two of our post-duplicates are found to be polymorphic in a recent survey of copy-number variation by Emerson et al. [47], but this number may be underestimated because of their experimental strategy: Because Emerson et al. designed their research to map the regions of copy-number variation on the reference genome of D. melanogaster, it might not be optimized to detect copy-number variation in the reference genome itself.

Here, we arbitrarily defined duplicated genes as those with synonymous divergence less than 0.2. This definition is to cover duplicate pairs that could potentially exchange DNA sequences frequently by gene conversion. This cutoff value should not be unreasonable, according to our previous theoretical work [15], together with the observation in yeast [11]: K_S for duplicated genes with evidence for gene conversion in yeast is usually less than 0.2. Our results are robust to this arbitrary cutoff value. For example, there is a very minor quantitative change in the estimate of gene duplication rate when the cutoff value is set as 0.3 because there are very few duplicated gene pairs with 0.2<K_S<0.3.

Selection after Gene Duplication

Neofuntionalization is one of the most important selective processes after gene duplication. To infer the action of natural selection, we first focused on the synonymous and nonsynonymous divergences (K_S and K_A) between duplicated genes, but we found no strong signature of selection for neofunctionalizations. There could be at least two reasons for this. First, such K_S−K_A analysis works best for relatively long-term molecular evolution, during which a substantial number of nucleotide substitutions accumulate. Therefore, the methods would not have sufficient statistical power for our data with recent duplicated genes, especially when active gene conversion between duplicated genes retards the paralogous divergence.

More importantly, gene conversion complicates the neofunctionalization process at the DNA level. When the duplicated genes undergo concerted evolution by gene conversion, which should be the case for many of the duplicated genes we analyzed, selection does not automatically result in the acceleration of nonsynonymous substitutions in the entire gene. The acceleration of substitutions will be limited to a narrow region around the target; therefore, K_S−K_A-based methods using the divergence in the entire gene should result in a lack of power. Instead, Teshima and Innan [24] suggested a possibility to focus on the spatial distribution of the divergence to detect signature of recent neofunctionalization. According to this idea, we found a strong signature in a pair of transporter genes (CG18281 and CG17637). This result indicates the promising possibility for applying this method as a genome scan for signatures of selection for neofunctionalization in other species. The advantage of our method is that it is possible to infer what parts of the genes are subject to selection.

Identification of Duplicated Blocks

Drosophila genome Release 3.1 (dm3) was used for the identification of duplicated genes. A total of 13,165 non-redundant protein sequences were in the database. All protein sequences were used as queries to search against all the others by using the BLASTP program with a cutoff value of e<10⁻¹⁰. We filtered out pairs of protein sequences with lower similarity than the criteria of Gu et al. [48], which is the protein identity α>0.3 if the alignable region β>150 bp, otherwise α≥0.06+4.8 β^{0.32[1+exp(β/1000)]}.

The duplicated genes detected in this screening process were aligned by using ClustalW [49]. The nucleotide divergence was estimated by using the method of Li-Pamilo-Bianchi [50],[51], and gene pairs with K_S>0.2 were screened out. In this analysis, we use 63 duplicated genes. Genes with no homologs with K_S<0.2 are considered as single-copy genes, and we found that the D. melanogaster genome has 12959 single-copy genes.

We identified the duplicated genomic regions (blocks) that involved those duplicated genes, using the BLASTN algorithm followed by visual inspection. The duplicated blocks were located on the latest version (Release 5.3; dm3) of the D. melanogaster genome, with the annotation data at the UCSC genome browser website (http://genome.ucsc.edu/). For these duplicated blocks, their orthologs were searched in other species in the D. melanogaster subgroup (Figure 1). All aligned sequences are provided in Dataset S1.

Phylogenetic Analysis

The DNA sequences of duplicated blocks in D. melanogaster and their orthologs were aligned together with an outgroup sequence from D. yakuba by using ClustalW [49]. Pairwise nucleotide distances [Kimura's distance, 52] were computed, from which an NJ tree was constructed (Figures S1 and 2).

Inferring the Original and Derived States of the Duplicated Blocks

For the post-speciation duplicated blocks, it may be possible to infer which of the duplicates the original copy was, if the intervening sequence between the duplicates is relatively long (i.e., I≫0). The intervening sequence was searched against the genome sequence of D. simulans (or D. sechellia). If the sequence has homology to the upstream of the D. simulans homolog, the downstream copy of D. melanogaster would be the original copy, and vice versa.

Statistical Test for Detecting Local Gene Conversion

For each block, we first estimated the number of nucleotide substitutions per site between the two orthologous pairs, p₀. Given this estimate, we consider k̅, the expected number of type-C sites in the duplicated block under a simple two-allele model with 0 and 1. The expected number of sites at which each of the X and Y regions experienced a mutation since speciation is roughly given by , where L is the length of the duplicated block. At such a double-mutated site, the resultant pattern of the two alleles (0 and 1) depends on the branches on which the mutations occurred. The left and middle trees in Figure 3C consider cases where the two duplicated regions had the same allele, 0, at the speciation event. In the left tree, both the two mutations occurred in the lineages leading to the same species (i.e., D. simulans in this example), so that the current allelic status for (X_m, X_s, Y_m, Y_s) is (0, 1, 0, 1) and the site becomes a type-C site. On the other hand, in the middle tree, the two mutations occurred in the lineages leading to different species (i.e., in this example, in the D. simulans lineage at X and in the D. melanogaster lineage at Y), resulting in (X_m, X_s, Y_m, Y_s) = (0, 1, 1, 0). This pattern cannot be explained by a single mutation even with gene conversion and is referred to as a type-M site in Figure 3A. Thus, because the probabilities that a mutation occurs in the two lineages are half at both X and Y, a double-mutated site becomes a type-C site with probability 1/2 when X and Y had the same allele at the speciation event. Similar logic holds for the case where X and Y had different alleles at the speciation event, and the probability to become a type-C site is again 1/2 (see Figure 3C). Therefore, the expected number of type-C sites is given by . Our statistical test examines whether the observed number of type-C sites is significantly larger than this expectation, that is, the P-value is given by(1)assuming the Poisson distribution of mutations.

For simplicity, we employed a two-allele model, although the real sequence has four nucleotides. This method underestimates the P-values because the probability that a double-mutated site appears as a type-C site is much smaller than 1/2: in most cases, it becomes a triallelic site. Thus, our treatment is conservative in terms of detecting gene conversion.

Detecting Signature of Selection

To detect signatures of selection, we used a sliding window approach. We set the window size = 200 bp. For each window, the numbers of type-C and type-N sites are computed, and compared with those in the surrounding regions (200 bp in each direction). In practice, a 2×2 contingency table is obtained and Fisher's exact P-value is computed. With a cutoff of P<0.0001, we found two peaks of the paralogous divregence, and both of them are in Pre28. A forward simulation was performed following Teshima and Innan [15], and it was found that a peak of divergence (>15% in a 200 bp window) appears in a 1600 bp region with probability <0.0001.