We predicted protein sequence errors, resulting from genome sequencing errors and exon/intron prediction errors, in the 14 high coverage vertebrate genomes (Table 1) from the Ensembl database, using a previously published method 37 . First, we constructed multiple sequence alignments (MSAs) for each of the 19,778 human protein sequences defined by the Human Proteome Initiative (HPI) and their potential vertebrate homologs. The sequences in the alignments were then clustered into more similar subgroups and errors were predicted if discrepancies were observed between one sequence and its close neighbours, for example between human-chimpanzee or between fish genomes. The error detection protocol was thus used to identify lineage-specific insertions, deletions or sequence segments, which are inconsistent with the conservation information in the MSA. Finally, we calculated the rate of sequence errors found in all 19,778 MSAs (Figure 2A). The MSAs contained a total of 344,437 protein sequences and 240,313 potential sequence errors, giving an estimated sequence error rate of at least 0.7 errors per sequence. The total number of sequences with at least one potential error was 142,836. Thus, on average 41% of sequences were predicted to be erroneous.

The observed error rates were not homogeneous across the different species. Lower rates were observed for the human and mouse proteomes, with 30-31% erroneous sequences, as might be expected for these well studied organisms. Among the non-human primate proteomes considered here, lower error rates were estimated for the orangutan (Pongo pygmaeus), compared to the chimpanzee (Pan troglodytes) and especially the Rhesus macaque (Macaca mulatta). The relatively high error rate for the macaque is not surprising since the macaque genome in Ensembl version 51 is a preliminary assembly using whole genome shotgun (WGS) reads from small and medium insert clones. On the other hand, the relative error rates in chimpanzee and orangutan are more surprising. Both the chimpanzee and orangutan genomes have been sequenced to 6x coverage, but in a recent study of primate genome assembly quality, the chimpanzee genome assembly was estimated to be of higher quality 38 .

Nevertheless, the same study found that about 70% of inferred errors in the orangutan genome were clustered in the 3.2% of the assembly that is of low quality, implying that > 96% of the assembly could be considered of high fidelity. We found the highest error rates in the opossum, chicken and fish proteomes, with > 45% erroneous sequences. Although these genomes have all been sequenced to high coverage, the lack of a well annotated reference genome from a closely related model organism may result in lower quality protein sequence prediction.

The predicted protein sequence errors were then characterized according to two different factors: (i) the nature of the error, i.e. insertion, deletion or suspicious segment and (ii) the position in the sequence, i.e. at the N/C-terminus or within the sequence. Figure 2B shows the proportion of the different errors observed. The most commonly found error was the presence of a suspicious sequence segment, possibly representing a mispredicted exon. At the N- and C- termini, deletions were observed more frequently than extensions. Although this may be due in part to the protocol used to detect sequence errors, it may also reflect the difficulty of predicting the first and last coding exons. In contrast, internal insertions were more common than internal deletions, suggesting that more internal errors were due to the over-prediction of introns as coding sequences, rather than the under-prediction of exons.

Putative orthologs were predicted for each of the 19,778 human proteins based on the MSAs of the human reference sequences and related sequences from the 13 vertebrate genomes. Two different approaches were implemented. First, the sequences from each organism with the smallest evolutionary distance were identified based on pairwise alignments extracted from the MSAs, and denoted "highest similarity homologs". Second, "syntenic homologs" were defined based on the local gene order conservation. The genome coverage achieved by the two methods is shown in Figure 3 and Table S1 in Additional file 1. The highest similarity homologs covered 80% of the 265,658 genes in the 13 vertebrate genomes, ranging from 89% in chimpanzee to 68% in zebrafish. As expected, a smaller proportion (43%) of homologs was found with locally conserved synteny, including 77% of chimpanzee genes and only 3% of zebrafish. Although our definition of locally syntenic regions is relatively stringent, we observe a comparable coverage to other existing methods. For example, we found 51% of mouse genes to be syntenic with human, compared to 59% using the method developed by 39 . Other more refined methods have been developed, such as Syntenator 40 , that use less stringent criteria to define conserved syntenic regions. By allowing more gene mismatches and gene insertions/deletions, Syntenator aligned 79% of mouse genes with human.

We then investigated whether the gene that is most similar on the sequence level is also the gene that shares the same gene-neighbourhood (Figure 3 and Table S2 in Additional file 1). Of the 212,409 similarity homologs identified in the 13 vertebrate genomes, 113,517 were found in locally syntenic regions. In mammals, this represents 69% of the highest similarity homologs. This is less than that estimated in a previous study 41 , where 97.5% of Inparanoid orthologs in human, mouse, rat and dog were found in syntenic regions, most likely due to our stricter definition of local synteny. On the other hand, only 1% of the identified syntenic homologs (1,157 out of 114,680) were not identified by the similarity-based approach. As expected, a generally higher level of disagreement was observed for more divergent genome pairs. Nevertheless, in human-chicken comparisons, the synteny method identified the same homolog as the similarity approach in 98.8% of the cases. Fewer consistencies were observed in human-fish comparisons (84-87% of syntenic homologs were also the highest similarity homologs), possibly due in part to the whole genome duplications in the fish lineage, resulting in a larger number of paralogs.

We then examined in more detail the 1,157 gene triplets (consisting of the human reference sequence and the two homologs representing putative orthologs in one of the 13 vertebrate genomes), where the syntenic homolog was not the same as the highest similarity homolog. To avoid including chance outcomes caused by very similar rates of sequence evolution of these homologs relative to the human sequence, we identified significantly different rates of evolution at the 95% confidence level (see Methods). Of the 1,157 gene triplets, a total of 688 corresponded to evolutionary scenarios where the syntenic homolog (i.e. the gene copy with the shared genome neighbourhood) evolved significantly faster (Table 2). A complete list of the 688 gene triplets is available in Table S3 in Additional file 1. The alternative scenario for asymmetric evolution where the remote copy evolved faster than the synteny copy is not detected by our protocol. since in this case the homologs defined by similarity and synteny would be the same.

The 688 gene triplets identified above, consisting of the human reference sequence, the highest similarity homolog and the synteny homolog, constitute a reliable test set representing potential asymmetrical evolution events. To study the impact of errors on the prediction of AED events, we identified erroneous sequences in this test set. Figure 4A shows the number of events that are assumed to be artifacts since at least one of the sequences was predicted to be erroneous, as well as the number of remaining 'true' events. Of the 688 gene triplets, only 294 (43%) do not contain erroneous sequences and may correspond to true events, while a total of 394 (57%) are putative artifacts.

As might be expected, the proportion of artifactual events varies with the different genomes studied, depending on the percentage of erroneous sequence detected (Figure 4B). For example, 19% of chimpanzee and 24% of mouse predicted events are due to artifacts, while this figure increases significantly for the draft macaque and chicken genomes (69% and 88% respectively). It is interesting to note that a larger proportion of artifacts are observed in the orangutan genome than in the chimpanzee, even though the orangutan genome is predicted to contain less sequence errors than the chimpanzee (see above).

In order to validate the putative protein sequence errors leading to artifactual AED events, we investigated the 413 predicted sequence errors in the human reference sequences and their syntenic homologs. The results of the analysis are shown in Table 3 and examples of the different errors detected are provided in Additional file 2. The majority (59%) of the erroneous sequences resulted from DNA sequencing or assembly errors, characterised by the presence of 'N' characters in the DNA sequences. For the remaining 171 protein sequence errors, we searched for the missing protein fragments in the corresponding DNA sequences. For errors involving missing segments (i.e. internal insertion, N/C-terminal extensions or suspicious segments), 89 of the 148 missing segments were detected and we therefore concluded that the error was due to an inaccurate gene structure prediction. In the case of sequence errors corresponding to inserted segments (internal insertions, N/C-terminal insertions), 16 of the 23 inserted segments were conserved in closely related organisms, although 5 of them had one or more stop codons. Finally, we manually verified the transcript evidence in Ensembl for all 23 insertions in gene sequences with no genome errors, as well as for the 59 unconserved deletions. Of these, 62 protein errors were not supported by any transcript information and 9 errors were due to the alternative splicing variants reported for homologous genes. Only 11 (2.7%) of the 413 putative protein sequence errors were identified as false positive predictions, since a transcript was found corresponding to the affected sequence segment.

To investigate whether the sequence errors leading to artifactual events were enriched for a particular type, we classified the errors into 7 types as described above. We then calculated the proportion of the different error types found in the gene triplets corresponding to the 688 predicted AED events (Figure 5). In the human reference sequences, only 32 errors were predicted, as might be expected since the human genes have been very widely studied. The majority (24 out of 32) of the human sequence errors were found at the N/C termini, with the exception of a small number of internal sequence segments that were labeled as being suspicious.

When all the sequences in the gene triplets were pooled, no significant enrichment was observed in the frequency distribution of the different error types causing artifactual events, compared to the background distribution observed in all the sequences (as shown in Figure 2). The goodness-of-fit was measured using a likelihood ratio chi-square statistic (chi-square = 3.12, p-value = 0.79). Nevertheless, different error types were observed when the syntenic and highest similarity homologs were considered separately. For example, artifactual events were observed more frequently if the syntenic homolog, i.e. the gene copy that retained the genome neighbourhood after duplication, contained suspicious segments. In contrast, N- and C-deletions in the highest similarity homolog, i.e. the gene copy that was relocated, were more likely to cause artifacts.

Figure 6 shows an example of an artifactual event observed in the gene triplet corresponding to [Swiss-prot:COPG_HUMAN] and the two homologs from macaque (the full length alignment is provided in Figure S1 in Additional file 1). The COPG protein forms part of the coatomer complex, involved in protein transport between the endoplasmic reticulum and the Golgi. The macaque syntenic homolog [Ensembl:ENSMMUP00000017291] contains a suspicious segment and an exon deletion that artificially increase its evolutionary distance to human, due to a low quality segment in the genome sequence (indicated by 'N' characters in the gene sequence). Consequently, another macaque protein [Ensembl:ENSMMUP00000006382] is identified as the highest similarity homolog of human COPG, resulting in an artifactual AED event prediction. In fact, [Ensembl:ENSMMUP00000006382] is the ortholog of [Uniprot:COPG2_HUMAN].

The orthology prediction method used in the Ensembl project, based on a phylogenetic gene tree approach, finds the correct 1-to-1 orthology relationship between the human and macaque COPG proteins. Unfortunately, many other orthology databases are less successful. For example, in the Inparanoid database (inparanoid.sbc.su.se), the Ensembl human COPG and macaque COPG2 sequences are in the same orthologous cluster, while no human ortholog is found for the macaque COPG sequence.

In order to investigate the effect of filtering the erroneous sequences on the subsequent functional analysis of asymmetrical evolution events, we conducted a gene ontology (GO) term enrichment analysis. Specifically, we investigated the 688 AED events detected in this work, where the local syntenic homolog was observed to evolve more rapidly than the relocated highest similarity homolog. At this stage, we excluded 81 events where the human reference sequence had more than one exon, but the relocated homolog had only one exon, since they are likely to be non-functional pseudogenes. For comparison purposes, we used two gene lists: (i) gene list 1 corresponding to the remaining 607 detected events, including both artifactual and putative true events and (ii) gene list 2 corresponding to 250 putative true events only (Table S4 in Additional file 1). The two gene lists were then analyzed for enrichment of GO terms using the AmiGO 42 web server, using the complete set of human genes as the background set and default parameters (Tables S5-6 in Additional file 1). The results of the AmiGO analyses were also submitted to the GO-Module 43 web server, in order to reduce the complexity and identify 'key' GO terms (Table 4).

Gene list 1 was enriched in 24 key GO terms, including a number of vertebrate specializations (e.g. anatomical structure development), but also some fundamental eukaryotic processes (e.g. regulation of metabolic processes, gene expression, axon guidance). For example, the term 'RNA biosynthetic process' is found with a P-value of 5E-16, involving 101 (20%) of the 607 genes in the list. However, only 6 of these 24 key GO terms are associated with the true events in gene list 2. Thus, the remaining 18 (75%) enriched GO terms are probably false positives resulting from the artifactual events. Furthermore, and perhaps more importantly, important key GO terms associated with the true events are not enriched in gene list 1, notably neurogenesis related functions. After filtering of gene triplets with erroneous sequences, gene set 2 was enriched in 10 key terms, including neuron differentiation functions, and response to the environment.

Figure 7 shows an example of a true AED event detected in the hepatoma-derived growth factor (HDGF) protein family. The HDGF and HDGF-like family members are characterized by a conserved PWWP domain in the N-terminal region. In human, the HDGF protein [Ensembl:ENSP00000349878] exhibits growth factor properties and has been implicated in organ development and tissue differentiation of the intestine, kidney, liver, and cardiovascular system. In addition, the role of HDGF in cancer biology has recently become a focus of research, since HDGF was found to be over-expressed in a large number of different tumor types (genecards.org). Whereas some family members, such as HDGF and HDGFL2, are expressed in a wide range of tissues, the expression of others is very restricted. For example, HDGFL1 and HDGFL4 are only expressed in testis, although their precise functions are still unknown. We observed an EAD event in several organisms, including mouse and rat. For example, mouse HDGFL1 [Ensembl:ENSMUSP00000057557] on chromosome 13 is syntenic with human HDGFL1 [Ensembl:ENSP00000230012] on chromosome 6, but mouse HDGF [Ensembl:ENSMUSP00000005017] shares higher sequence similarity with human HDGFL1 (58% identity versus 53%). Although mouse HDGFL1 is specifically expressed in testis, like human HDGFL1, the human and mouse proteins are more divergent in the C-terminal region and probably have different functions. In fact, mouse HDGFL1 lacks the caspase cleavage site identified in mouse HDGF, as well as a number of conserved residues that are known to be phosphorylated (genecards.org).

We detected erroneous protein sequences based on discrepancies in the conservation of vertebrate protein MSAs. The sequence errors may result from (i) DNA sequencing errors, (ii) badly predicted introns/exons, (iii) different splicing variants predicted in different organisms. We estimated the frequency of erroneous sequences to be at least 41%, although some genomes are more error-prone than others, depending on factors such as sequencing coverage or the availability of a well annotated genome from a closely related organism.

In this study, we only considered sequences from the Ensembl database and we used cross-comparisons between species to identify discrepancies. However, Ensembl may produce predictions that are consistent across organisms, i.e. may reproduce the same errors in different genomes or propagate intron/exon structures. Thus, our estimate of the average sequence error rate is probably conservative. Another recent study 51 showed that the Ensembl compara sequence prediction method correctly identified only 55% of coding transcripts exactly.

Our main goal was to determine to what extent these erroneous sequences affect subsequent evolutionary analyses. We focused on a specific event: gene duplication and the evolutionary fate of paralogs, since gene duplication is often assumed to be the most important source of new functions.

Since duplication events where the local copy has evolved more rapidly may indicate unusual evolutionary scenarios, innovations or adaptations, we specifically searched for examples of such asymmetric evolution events. Our approach involved the identification of reliable AED events that could be used as a test set for estimating the impact of sequence errors. We therefore designed a stringent protocol where we included only high coverage genomes and used the well studied human genome as a reference. We then identified putative orthologs in 13 vertebrate genomes, based on either sequence similarity or local synteny conservation. The similarity-based method used a very simple model of sequence evolution, in order to avoid bias towards one particular model. Nevertheless, this model clearly oversimplifies the complex evolutionary processes involved, and in the future, it would be interesting to investigate the effect of a more realistic model of sequence evolution on AED detection, once sequencing/annotation errors have been removed. We also used a strict definition of local synteny, which led to lower genome coverage in the ortholog prediction step. For the detection of asymmetric evolution, we used a simple measure of amino acid divergence and specified a high significance threshold that would ensure only reliable predictions. Nevertheless, 688 putative AED events were identified that were then used to perform an in-depth investigation of the effect of sequence errors.

We compared the syntenic and highest similarity homologs and identified cases where significantly faster evolutionary rates were observed in the syntenic homolog, i.e. the gene copy that retained the genome neighbourhood after duplication, compared to the relocated highest similarity homolog. Initially, 688 AED events were identified, of which 81 similarity homologs were potential retropseudogenes with a reduced exonic map. The majority (57%) of the remaining detected events corresponded to erroneous sequences and only 250 represented putative true AED events. Thus, we conclude that care should be taken when performing genome-wide scans to search for genes with unusual patterns, since outlying genes are more likely to be due to artifacts in the input sequences than the result of true evolutionary events. Furthermore, our in-depth study revealed some of the mechanisms by which errors in the input sequences are propagated during the event prediction. For example, a badly predicted internal segment in one of the homologs results in an increased evolutionary distance to the human reference sequence, while a loss in the more variable N/C-terminal regions artificially reduces the distance. These observations provide guidelines for future error detection and correction strategies that will hopefully allow us to reduce the impact of the sequencing errors.

In asymmetric evolution, one duplicate evolves or degrades faster than the other and often becomes functionally or conditionally specialized. In this context, the accurate detection of the 'functional' homologs, i.e. protein pairs that play functionally equivalent roles 52 , is critical. We have shown that orthology assignment and the detection of important genetic events are severely impacted by the high proportion of errors in the initial set of protein sequences, even in high coverage genomes. The errors in the initial data are accumulated and amplified in the higher-level analyses. Our estimated rate of 41% erroneous protein sequences leads to 57% errors in AED event prediction and, in the subsequent Gene Ontology (GO) functional analysis, 75% of the enriched terms are in fact false positives.

The false positive terms in the functional analysis can be very costly to investigate experimentally and a reduction in the false discovery rate is clearly desirable. They are also sufficient to mask some of the true functional enrichments. After filtering the artifactual events corresponding to erroneous sequences, the remaining AED events were enriched in a number of GO categories, including neuron differentiation and response to external stimuli. Interestingly, human-specific duplicates evolving under adaptive natural selection also include genes involved in neuronal and cognitive functions, as well as response to inflammation or stress 53 . Similarly, gene families involved in copy number variations (CNVs) are enriched for similar categories, including interactions with the environment, neurophysiological processes and brain development 54 . A recent study suggested that the relationship between CNVs and positive selection may play an important role in the emergence and evolution of species-specific traits in primates 55 . Genes in many of these categories are thus thought to be important in evolutionary adaptation and to be particular targets of natural selection.

Human protein coding genes were retrieved from the Human Proteome Initiative (HPI) and Swiss-prot databases 56 , resulting in a total of 19,778 human sequences. Each gene was then used as a query for a BlastP 57 search in a database consisting of the proteomes of 14 vertebrates (Table 1) with almost complete genomes from the Ensembl (version 51) database 36 . The Ensembl human protein sequence with the highest similarity to the HPI query was designated as the reference protein sequence. For each of the 19,778 human reference sequences, potential orthologs were then identified using two different, complementary approaches: sequence similarity and local synteny.

For each human reference sequence, a modified version of the PipeAlign 58 protein analysis pipeline was used to construct a multiple sequence alignment (MSA) for all sequences detected by the BlastP search with E < 10^-3 (maximum sequences = 500). PipeAlign integrates several steps, including post-processing of the BlastP results, construction of a MSA of the full-length sequences with DbClustal 59 , verification of the MSA with RASCAL 60 and removal of unrelated sequences with LEON 61 . In this modified version, DbClustal was replaced by the MAFFT 62 program, since the computational speed of MAFFT is better suited to high throughput projects. The MSAs obtained from this pipeline were then annotated with structural and functional information using MACSIMS 63 , an information management system that combines knowledge-based methods with complementary ab initio sequence-based predictions. MACSIMS integrates several types of data in the alignment, in particular Gene Ontology annotations, functional annotations and keywords from Swiss-prot, and functional/structural domains from the Pfam database 64 .

Based on the MSA, the evolutionary pairwise distance, d, between any two sequences was defined as the number of amino acid substitutions per site under the assumption that the number of amino acid substitutions at each site follows the Poisson distribution. Thus:

d = - ln 1 - p

where d is the pairwise distance and p is the proportion of different amino acids aligned (dissimilarity).

Then, for each human reference sequence, H_i, the sequences from the 13 vertebrate organisms with the highest similarity (i.e. the smallest distance) to H_i were identified and denoted Vn_Sim_i, where Vn refers to one of the 13 vertebrate organisms (Figure S2A in Additional file 1).

The chromosomal localization of all genes coding for protein sequences was obtained from the Ensembl database. Locally developed software was used to identify regions on the human chromosomes where local synteny was conserved between the human genome and each of the other 13 vertebrate genomes. The chromosomes in each genome are thus represented as a linear sequence of genes. For each human reference sequence, the local syntenic homolog was defined as outlined in (Figure S2B in Additional file 1). For the coding gene, H_i, at position i on the human genome, its neighbours (H_i-1 and H_i+1) were identified. For each of the 13 vertebrate genomes, the sequences with the highest similarity to H_i-1 and H_i+1 were selected from the MSA as described above, and denoted Vn_Sim_i-1 and Vn_Sim_i+1 respectively, where Vn refers to one of the 13 vertebrate genomes. A local synteny homolog, Vn_Syn_i exists for H_i and genome Vn if: (i) homologs were found in Vn for H_i-1 and H_i+1, (ii) the separation between the highest similarity homologs, denoted Vn_Sim_i-1 and Vn_Sim_i+1, on the genome was less than 5 genes and (iii) a homolog of H_i was found on the genome between Vn_Sim_i-1 and Vn_Sim_i+1. The homolog of H_i localized between V_Sim_i-1 and V_Sim_i+1 with the highest similarity (smallest evolutionary distance) to the human reference sequence was then defined as the syntenic homolog.

Genes with ambiguous genomic locations, such as scaffolds etc., were discarded since the synteny relationship could not be reliably established. In addition, local or tandem duplications were excluded since the genome contexts of the two gene copies were similar. Although tandem duplicates should be adjacent to each other on one chromosome, extensive gene inversions may insert irrelevant genes into the tandem arrays. We therefore used a stringent threshold and excluded cases where Vn_Sim_i and Vn_Syn_i were separated on the genomes by less than 10 genes.

For each MSA corresponding to a human reference sequence, an automatic protocol was used to detect sequence discrepancies that may indicate gene prediction errors. Different types of prediction error were considered, such as excluding coding exons, including introns as part of the coding sequence, or wrongly predicting start and termination sites. The protocol is described in detail elsewhere 37 . Briefly, the sequences in the MSA were first clustered into more related subfamilies then, for each subfamily, sequences with potential errors were identified using an empirical rule-based approach. (i) Badly predicted exons were identified using the RASCAL algorithm 60 as outliers or 'suspicious' sequence segments (Figure 8A). (ii) Badly predicted start or stop sites were identified by considering the positions of the N/C-terminal residues for each sequence in the subfamily alignment (Figure 8B). Normal values were defined as lying within the lower and upper quartiles of the distribution of terminal positions. Sequences with terminal positions outside this window were annotated as potential deletion/extension errors. (iii) Inserted introns (Figure 8C) were detected if a single sequence contained an insertion of more than 10 residues. (iv) Missing exons (Figure 8D) were detected if a single sequence contained a deletion of more than 10 residues.

Each error was then classified in one of 7 different classes: internal insertions, internal deletions, suspicious sequence segments, extensions at the N- or C-terminus, and deletions at the N- or C-terminus.

The errors in the protein sequences were estimated by analysing the corresponding DNA gene sequences from the Ensembl database. First, if the gene sequence contained a run of 'N' characters, we assumed that the predicted protein sequence error was the result of a DNA sequencing or assembly error. Second, the gene sequences with no 'N' characters were searched for the missing protein sequence fragments. For errors corresponding to internal deletions, deletions at the N- or C- terminus or suspicious sequence segments, the missing protein fragment was extracted from a closely related sequence in the multiple alignment. The protein fragment was then aligned to the gene sequence from the ENSEMBL database using the PairWise software 65 . The fragment was considered to be present in the gene sequence if the percent identity of the protein and translated gene sequences was greater than a given threshold. The threshold used here was specific to the pair of organisms compared and was defined as the lower quartile of the protein sequence identities for the complete proteomes of the two organisms. A similar protocol was used for the errors corresponding to insertions in a given protein sequence, except that, in this case, the protein fragment corresponding to the insertion was aligned to the gene sequence of another closely related sequence. Finally, the transcript evidence for the protein sequences in the Ensembl database was searched manually for known transcripts and splicing variants.

It has been suggested that, after a gene duplication event, one duplicate generally maintains the ancestral function while the other is free to evolve and acquire novel functionality. This scenario implies that the protein with conserved functionality will undergo less sequence evolution than the one exploring new functionalities. To determine which of the two homologs described above (highest sequence similarity or syntenic) was more likely to share the same function as the human reference sequence, we estimated the difference between the two evolutionary distances: human reference to similarity homolog and human reference to syntenic homolog. Thus, for each of the 13 vertebrate genomes considered in this study, we have a triplet of homologs, H_i, Vn_sim_i, Vn_syn_i, and we want to estimate the difference Δ between two distances d(H_i, Vn_sim_i) and d(H_i, Vn_syn_i).

We used an estimator based on pairwise sequence distances similar to one defined previously, that is relatively fast to compute and has almost the same statistical power as the widely used maximum likelihood estimator 66 . The distance, d, between two sequences is defined as the number of amino acid substitutions per site under the assumption that the number of amino acid substitutions at each site follows the Poisson distribution, as before. The variance σ of the distance d is given by:

σ 2 d = p ∕ 1 - p n

where p is the proportion of amino acid differences and n is the total number of amino acids compared.

If X has two homologs Y and Z, and Y is the closest homolog to X, an estimator for the difference in evolutionary distances is:

Δ = d X , Y - d X , Z

The variance of the difference can be computed as:

σ 2 Δ = σ 2 d X , Y + σ 2 d X , Z - 2 c o v d X , Y , d X , Z

and thus, an upper bound for the variance of the estimator is:

σ 2 Δ = σ 2 d X , Y + σ 2 d X , Z

Finally, we assume X,Y are significantly closer than X,Z if:

Δ < - k . σ Δ

In this work, the parameter k was set to 1.96, reflecting the 95% confidence level. Thus, we would expect 5% of the tested gene triplets to falsely reject the hypothesis of asymmetrical evolution.