An impressive number of methods for the identification of CA and pA genes was introduced so far; e.g. 11161718, see also 7. In order to compare the predictive power of methods and to evaluate the new approach, I used as a test set the genes annotated on chromosome two of V. cholerae. This chromosome contains an integron island of size 125.3 kbp, which includes genes VCA0271 to VCA0491 19. For the analysis, two groups were formed consisting of genes VCA0010 to VCA0230 (group cl) and genes VCA0271 to VCA0491 (group gi). For each gene, codon usage contrast, δ* difference, dicodon difference – as defined in 18 – and h_MPW(gene) as described in Methods were determined. These scores were accumulated parameter-wise in pairs of histograms H_cl and H_gi. The decision-strength of each parameter was assessed by incrementing a running cut-off c_o_r and reading from H_cl and H_gi the fraction of genes accumulated below c_o_r. Resulting curves are plotted in figure 1. The experiment clearly shows that the new algorithm outperforms the methods, which evaluate deviation from mean frequencies of codons, dicodons or dinucleotides. In addition, the plot demonstrates that codon usage contrast (in the following abbreviated as CU) is the second best indicator on the test set.

Lawrence and Ochman 14 have developed a surrogate method that combines analysis of GC-content on the first and third codon position, of synonymous codon usage, of positional homology and of BLAST hits (in the following abbreviated as CA_LO). The results achieved for the E. coli K-12 genome are available ftp://ftp.pitt.edu/dept/biology/lawrence. In figure 2, for all genes of this genome, GCB scores – signalling translational efficiency 20 – were plotted vs. CU-contrast and MPW score values. 402 of the 569 genes annotated as CA with the MPW-approach were also classified as CA_LO. This number of coincidences is the 4-fold of the fraction expected to occur merely by chance and is much higher than the overlap of any two other methods tested so far; see 6. Therefore, it can be deduced that a significant portion of the CA genes were acquired via HGT and that the periods of genomic evolution addressed by the CA_LO and the MPW approach overlap to a great extend. The plot makes also clear that putatively highly expressed (PHX, see Methods) genes have to be excluded in applying surrogate methods. At least some of the genes identified as compositional atypical with the CA_LO method were PHX. Because of the highly specific codon usage, it is unlikely that these genes have been acquired via HGT (see figure 2).

It is known that the number of pA genes varies significantly among microbial genomes 21. Some reasons explaining these differences are the nature and the efficiency of the transformational system or the assortment of the ecological niche the species occupy. In table 1, for a number of species the fraction of CA genes is given and compared to values published for HGT. For most of the genomes listed in 21, the fractions of genes identified as compositional atypical are similarly high. The MPW approach identified for the genomes of Synechocystis (CA_LO = 16.6% / MPW = 5.6%) and A. aeolicus (9.6% / 3.3%) a lower and for A. pernix (3.2% / 6.1%) a higher amount of CA genes. For the genomes of M. leprae, T. thermophilus, A. fulgidus, C. acetobutylicum, P. horikoshii, Halobacterium, B. burgdorferi, A. aeolicus and Nostoc, the fraction of CA genes was below 5% and for the genomes of B. melitensis, C. crescentus, M. jannaschii, T. pallidum, C. jejuni, M. thermautotrophicus, M. kandleri, P. aerophilum, C. perfringens, T. elongatus, R. conorii and C. muridarum, it was below 3%. This was also true for the genomes of D. radiodurans and H. pylori, which is in contrast to already published findings 21. In the genomes of N. meningitidis, R. prowazekii, F. nucleatum, Buchnera, M. genitalium, M. pulmonis and U. urealyticum the fraction of CA genes was below 1%. These values correspond well with findings concerning the mosaic structure of genomes: In N. meningitidis only 2.2% of the genome are meningococcus specific 22. In the sequences of many microbial genomes, a noticeable skew in the usage of guanosine and cytosine residues is detectable and frequently used to identify the origin of replication. An extensive survey of genomes based on such methods 2 identified six chromosomes not presenting a significant structure: Those of Nostoc, Synechocystis, Buchnera, R. conorii, B. burgdorferi and A. aeolicus. Clusters of pA genes with deviating codon usage would presumably influence the local GC-content, which is obviously not the case in the considered genomes. The two chromosomes of R. solanacearum (>10% of CA genes each) have both a mosaic structure 23.

The genome of B. subtilis has been assessed using a system of hidden Markov models in order to detect heterogeneities in DNA composition 24. Table 2 is an extended version summing up these findings and the location of CA clusters identified with the MPW approach. The table demonstrates that both algorithms identify with similar efficiency regions of deviating DNA composition.

In a critical survey, four surrogate methods were compared 6 by studying the intersections of those sets of genes identified as pA by the various methods. It turned out that only the CA_LO approach and a method based on hidden Markov models tagged the same genes as pA more frequently than expected by change.

In 25, the genomes of two Xanthomonas pathogens were compared: Xanthomonas axonopodis pv. citri (Xac) and Xanthomonas campestris pv. campestris (Xcc). To identify unique genes the authors BLASTed each gene of one genome against all genes of the second one and analysed the hits. For the following comparison those genes were named unique that had no BLAST hit with an E-value < 10^-20 in the second genome. These data sets were downloaded from http://cancer.lbi.ic.unicamp.br/xanthomonas. As the MPW approach was designed to predict clusters only, unique genes lying isolated were removed. The resulting data sets were compared against the MPW prediction. For Xac, 425 genes were identified as unique; the MPW approach annotated 488 genes as CA. 248 genes were both unique and CA. In the Xcc data set consisting of 4240 genes, 340 had the attribute unique and 454 the attribute CA, 213 genes had both attributes. If these attributes were completely unrelated, one would expect for Xcc the following number n of genes with both attributes: n = (454/4240 × 340/4240) × 4240 = 36. In both genomes, the number of CA genes labelled as unique is more the five times the expected value.

Altogether, these findings support the notion that the MPW approach identifies to a great extend the same class of genes as hidden Markov models or the CA_LO method. An example for a summary view of SIGI's output is given in figure 3.

Beginning with the acquisition of an alien gene, its codon usage will be modulated depending on selective constraints and mutational pressure affecting the recipient's genome. This process was named amelioration 14. One might argue that the codon usage of an ameliorating gene differs significantly from both the donor's and the acceptor's codon frequencies and may thus cause false predictions. In order to test the robustness of the MPW approach with respect to the amelioration process, synthetic genes consisting of random codon sequences of different length between 100 and 500 codons were generated. Each test set consisted of 500 sequences. Codons were selected randomly according to the frequency values as deposited in the CUTG_RF database (see Methods). For each test set, two species REC (recipient) and DON (donor) and a value FRAC (0.0 ≤ FRAC ≤ 1.0) were chosen. Codons were drawn according to the frequency tables CDN_REC or CDN_DON. FRAC determined, how often CDN_DON was selected as a source for the determination of codons frequencies. For the analysis described below, for each combination of a donor and an acceptor, nine data sets were generated according to the FRAC-values 0.0, 0.05, 0.10, 0.25, 0.50, 0.75, 0.90, 0.95, 1.0. These test sets served as a crude model for the amelioration process of genes originating from the donor in the recipient's genome. Test sets were generated for four species. M. loti (GC-content 63%), E. coli K-12 (GC-content 52%), P. horikoshii (GC-content 42%) and C. acetobutylicum (GC-content 31%) were used as acceptors and different genomes were selected as donors. The donors were chosen individually, according to phylogenetic relation and their similarity in codon usage with respect to the acceptor. Table 3 lists these combinations used to generate synthetic genes.

It is known that the mean GC-content at the three codon positions is correlated with the mean GC-content of the genome 26. A significant deviation of the position-specific GC-content from expectation values derived from the mean GC-content of a gene was interpreted as a signal identifying ameliorating genes 14. In order to determine a precise measure for the calculation of position-specific GC-values, 89 microbial genomic data sets were analysed and used for linear regression. The following formulas were deduced:

GC_{exp 1} = 0.761 GC_mean + 17.9

GC_{exp 2} = 0.481 GC_mean + 15.6

GC_{exp 3} = 1.732 GC_mean - 33.0

GC_mean is the mean GC-content of a gene set under study; GC _{exp 1} .. GC_{exp 3} are the expected GC-content values of codon positions 1 to 3. To evaluate the GC composition of a gene, expectation values GC_{exp i} as indicated above were derived from its mean GC-content and compared to the position-specific values GC_i. An indicator already used to signal amelioration 14 is the Manhattan distance GC_dist assessing codon positions 1 and 3:

The underlying model implies that the mean GC_dist value is larger in the midst of the amelioration interval. The mean deviation should be minimal for newly acquired genes or those having nearly gained the donor's composition. Thus, one might expect that genes with high GC_dist values generate the largest number of false predictions. In table 4, which summarizes the results obtained for predicting the putative source of synthetic sequences, only entries having a GC_dist value below the cut-off value AMELI were analysed via the MPW approach. AMELI was incremented from 0.05 to 0.25. A putative source was regarded a wrong prediction, if it was neither a taxon linking the donor with the root of the taxonomic tree nor a taxon linking the acceptor with the root. The presented predictions were derived from the taxonomical relation of the k = 3 highest scoring species (see Methods). Consequently and in the worst case, the term "cellular organism" or the name of a superkingdom was predicted as the putative source. Predictions based on k = 2 pairwise scores were in many cases wrong (data not shown). Interestingly, the number of false predictions is extremely low, if the acceptor's GC-content is above 40% and if the Manhattan distance to the acceptor's codon usage is below 15. The results obtained for FRAC = 0.95 clearly indicate that the algorithm is robust as long as the codon usage is species-specific: Among 24 cases, only the combination of the acceptor M. loti and the donator F. nucleatum generated more than 20% false positive predictions.

If the random sequences used for the analysis are a proper model for the amelioration process, then the following problem arises: The result suggests that the amelioration of a sequence originating from a species with very dissimilar codon usage causes misleading signals. In addition, the results presented in table 4 do not show a correlation of the relative number of false positive predictions with the GC_dist value. Therefore, and at least for the data set used here, the interpretation of the GC_dist value was no indicator to identify ameliorating sequences. If ameliorating sequences of that kind were frequent in genomes, then the interpretation of codon usage or signatures as in 27 would be questionable. However, there is one argument that might resolve the dilemma: It was made plausible that the range and the frequency of HGT is constrained by selective barriers 15 and one might expect that a codon usage too dissimilar to the acceptor's one prevents an expression level necessary to guarantee the survival of a gene in the acceptor's genome.

A second test for the predictive power was based on the analysis of native genes selected in 20 species representing the bacterial and archeal superkingdoms. From the genomes of A. fulgidus, M. acetivorans, T. acidophilum, P. horikoshii, T. maritima, D. radiodurans, C. glutamicum, L. lactis, S. pneumoniae, B. subtilis, E. coli, Y. pestis, H. influenzae, N. meningitidis, H. pylori, A. tumefaciens, M. loti, R. conorii, C. pneumoniae and M. pulmonis, genes annotated by SIGI as putative native ones were extracted. Each data set consisted of more than 200 genes. During the analysis and for all data sets, each of the mentioned species was regarded as the putative acceptor resulting in 20 × 20 individual tests. For all genes, the putative source was predicted individually as described (see Methods). In 14 of the 20 data sets, the highest score identified the source correctly for more than 90% of the genes on the level of the taxonomical family irrespective of the choice of the putative acceptor. Less specific were the results for the data sets extracted from the genomes of L. lactis (72% correct predictions on the family level), S. pneumoniae (81%), C. glutamicum (88%), B. subtilis (88%), Y. pestis (83%) and from genes of chromosome 1 of D. radiodurans (59% correct predictions on the phylum level). Inferring the putative source from three high scoring pairwise comparisons as described below, reduced – as expected – the specificity of the taxonomical classification. However, the number of false predictions decreased drastically: For all cases besides D. radiodurans, less than 5% of the sources were misclassified on the level of the taxonomic class. In the worst case, i.e. for D. radiodurans genes, 32% of the predictions were wrong on the phylum level. These findings suggest that codon usage in the extracted gene set of D. radiodurans is unspecific and has to be studied in more detail. In no case, more than 1% false classifications were generated on the level of the superclass. This result indicates that codon usage in Bacteria and Archaea is quite distinct.

It is known that genomic islands are inhomogeneous in composition and have a mosaic structure, as they are the result of a multistep process 8. For a first analysis of the genomes however, I identified genomic islands annotated relatively homogeneously with respect to the putative donor.

Each Salmonella genome has approximately 12 fimbria operons frequently involved in virulence 28. In S. typhimurium, the operons fim, saf, std and sth were identified as CA, bcf, lpf, stc, stf, sti and stj were silent. In S. enteritidis, sef, stb, std, ste and tcf were identified as CA, bcf, saf, sta, stc, stg and sth were inconspicuous. The integrated phage genomes Gifsy-1, Gifsy-2, Fels-1 and Fels-2 were CA. In many cases, for these islands the taxa "Bacteria" or plasmids are predicted as putative source, indicating an unspecific codon usage. The bias seen in the fimbria operons might be due to the strong selective pressure imposed by the host immune system. Based on the analysis of the ycdB gene, it was claimed that genomic islands of low GC-content were acquired from Lactococcus lactis 29. SIGI gave the following annotations for the most similar sequences of ycdB: AAC75047 of E. coli K-12 predicted as CA originating from Bacilli, second most similar codon usage (hit) Lactococcus, CAD06974 of S. enteritidis CA (Bacilli, first hit Lactococcus), AAL23317 of S. typhimurium was not annotated as CA, SF2054 of S. flexneri CA, (Bacilli, first hit Lactococcus).

In Salmonella enterica, several CA clusters were identified. In the following list, for some clusters the positions, gene names, coded proteins and putative sources are given: 1004 kb – 1053 kb contains genes annotated as putative bacteriophage proteins, originating according to SIGI from plasmids or Enterobacteriaceae; 1625 kb – 1651 kb, ssa genes, coding for a type III secretion system, Enterobacteriaceae; 2118 kb – 2135 kb, rfb, putative transferases, inhomogeneous codon usage; 2863 kb – 2900 kb, prg and sip, pathogenicity 1 island effector proteins, spa, surface presentation of antigens, inv, secretory proteins, Enterobacteriaceae; 3830 kb – 3838 kb, ccm heme exporter protein, Proteobacteria; 3930 kb – 3941 kb, waa, involved in the lipopolysaccharide core biosynthesis, Enterobacteriaceae; 4403 kb – 4543 kb, topB, a topoisomerase, pil, vex polysaccaride export, Enterobacteriaceae, plasmids.

The codon usage of most CA genes identified in Bacillus subtilis (see table 2) is unspecific. If SIGI predicts a specific taxon, it is a closely related clade. A similar result was observed for the genome of Escherichia coli O157:H7. 728 genes were identified as CA, the codon usage table causing the highest score was in 137 cases derived from a plasmid, 349 times it was from a species belonging to the gamma subdivision. All prophages and prophage-like elements known to be integrated into the genome 30 were found plus several additional CA clusters. All known pathogenicity islands of V. cholerae are CA, among these were the recently identified islands on chromosome one, named "seventh pandemic islands" 31. For a detailed analysis, see the material deposited on our webserver.

In the genome of the α-Proteobacterium Caulobacter crescentus, only 2.5% of the genes are CA. Several genes clustered in the area from 621 kb – 694 kb were predicted as originating from the Rhizobiaceae group: CC0575 coding for a putative beta-lactamase (p1 = 5 × 10^-4, p2 = 9 × 10^-5), CC0576, it's product is an asparaginase family protein (p1 = 0.01, p2 = 9 × 10^-5) or CC0618, cysG coding for a siroheme synthase (p1 = 0.01, p2 = 9 × 10^-5). The indices p1 and p2 are explained in Methods. A second cluster at 2.90 kb – 2.95 kb contains the genes for the conjugal transfer protein trbI and several transposases. The codon signature is inhomogeneous, dominated by species of the Rhizobiaceae group.

Haemophilus influenzae Rd is a small, Gram-negative bacterium; the only natural host is human. For 15 genes, the γ-Proteobacterium Shewanella was predicted as putative source. 12 of these hits were clustered in the region 1572 kb – 1590 kb which belongs to an island extending from 1555 kb – 1595 kb. It contains among genes for hypothetical proteins fepC and genes coding for Mu proteins like muA. Recently, a Shewanella species was identified as human pathogen 32 making the prediction plausible. As the GC-content of H. influenzae is 38%, these predictions have to be interpreted with care (see above, results for ameliorating genes).

In many cases, restriction-modification enzymes were identified as CA like in Nostoc. A genomic island (3278 kb – 3289 kb) containing a type 1 restriction modification enzyme follows a tRNA-Ala gene and a transposase. A second enzyme of that type is located in the genomic island (4186 kb – 4220 kb) following a tRNA-Gly. These genes are predicted as originating from Bacilli and Chlamydophila.

In the genome of Streptococcus pyogenes, 131 genes are annotated as "phage associated". However, only 50 of these genes were identified as CA. A CA island spans from 884 kb to 895 kb containing a putative methyltransferase and the srt system involved in lantibiotic production; the putative source is diffuse.

It is known that the genome of Mesorhizobium loti contains a huge symbiosis island (4645 kb – 5256 kb) of size 611 kb 9. SIGI predicts most of these genes as originating from the Rhizobiaceae group. The hypothetical protein MLR6371 has the codon signature of the beta subdivision. Examples for additional CA clusters are: 341 kb – 362 kb coding for unknown proteins around a bacteriophage integrase, genes are similar in codon usage to plasmids and Rhizobiaceae; 779 kb – 827 kb codes several transferases; 843 kb – 861 kb containing genes for an adenylate cyclase, putatively originating from the Rhizobiaceae group (p1 = 0.04, p2 = 3 × 10^-5) and rsp, the rhizobiocin secretion system; 2592 kb – 2610 kb containing a cyclase and a glycosyltransferase gene; 3219 kb – 3234 kb with genes for a DNA invertase rlgA and an excisionase; 3705 kb – 3755 kb containing genes for a glycosyltransferase, a DNA polymerase, chloramphenicol-acetyltransferase, heat shock proteins, codon usage most similar to Rhizobiaceae group; 5714 kb – 5742 kb containing genes for elements of an ABC-transporter, methyltransferases, hydrolases; 6580 kb – 6681 kb genes for hypothetical proteins, an ABC-transporter, a DNA modification-methylase, a histidine-kinase and a site-specific recombinase, the codon usage is most similar to that of the Rhizobiaceae group.

For a complete listing of the results, see the material deposited on the web server http://www.g2l.bio.uni-goettingen.de. For each genome, results are available in a tabulated version and a format readable by the gene browser ARTEMIS 33.

The simplest statistical model describing genes as a sequence of codons assumes that codons occur independently from each other. For this model, the Neyman-Pearson lemma assures that a function of the type

is optimal to decide, whether gene = start codon, cdn₁, ccdn₂......cdn_n is a member of the family G1 characterized by codon frequencies f_G1 (cdn_j) or belongs to family G2 having codon frequencies f_G2 (cdn_j). As a result of test theory, it is known that there exists no other function with a decision strength greater than expression (I). Applying the logarithm and normalizing for gene length gives:

Now h(gene) is the sum of species-specific log-odds scores PW_G1G2(cdn) divided by the number of codons constituting the gene. Scores of that type were utilized frequently and are supported by a sound theory 43. Recently it was shown that a similar approach is appropriate to quantify codon usage bias associated with translational efficiency 20.

The score values PW_G1G2(cdn), which were here always deduced from codon frequencies among synonymous codons, can be used to decide whether codon usage in gene resembles more the prevalences of species G1 or species G2. If gene is from genome G1 and if h(gene) is >> 0 then its codon usage is more similar to G2. Therefore, and if G2 is taxonomically distinct, the gene under study must be regarded an alien gene and genome G2 might be its source. In the study presented here, a putative source was predicted for genes longer than 100 codons only. This lower limit for gene length was introduced in order to reduce statistical variation due to small sampling size.

As it was one aim of the study to predict the putative source of compositional atypical genes, it was necessary to generate a sufficiently large number of score sets covering most of the possible origins of taxonomically related species. A prerequisite for the calculation of these scores PW_G1G2 are codon usage tables. Their compilation was initiated with data sets derived from completely sequenced microbial genomes, which were publicly available. Frequency values f_G2(cdn_j) were determined from those genes not annotated as hypothetical or with a putative function. It is known that codon frequencies in putatively highly expressed (PHX) genes deviate significantly from mean values 344. For each gene, z-scores were determined for CU contrast 18 and GCB-values 20 (compare figure 2). A gene was regarded as PHX, if the combination of the two scores exceeded a predefined cut-off value. This initial set was supplemented with entries from the CUTG database 45 in the version as of Aug. 2002. From this collection, only those microbial entries were accepted that contained more than 6400 codons. If more than one frequency table existed for the same taxonomic species, the data set deduced from the largest number of codons was processed further. After data collection, similarity of codon usage among species was controlled by calculating pairwise a Manhattan-like distance among codon usage tables. This distance values were used to select the final set CUTG_RF of codon frequencies. For all elements of CUTG_RF, it was confirmed that the most similar species on codon usage belongs to the same taxonomic class or superclass. This step and the other precautions mentioned above were introduced in order to guarantee taxonomic relatedness among the entries and to eliminate codon usage tables presumably derived from a non-representative sample of a genome. The collection was supplemented with codon usage tables of plasmids. Altogether CUTG_RF consisted of n_RF = 371 entries used for the calculation of scores PW_G1G2(cdn) at position G2. The codon frequencies f_G1 (cdn_j) of the genome G1 under study were determined from those genes not annotated with the terms "hypothetical" or "putative" and which were no PHX genes.

For the analysis of each gene of a genome G1, its codon usage was evaluated in a multiple pairwise test (MPW) using n_RF individual scoring schemes PW_G1G2(cdn). The species G2_max causing the highest score h_MPW(gene) was considered a putative source, if h_MPW(gene) exceeded a cut-off value. In order to quantify the statistical relevance of the prediction, two parameters p1 and p2 were introduced. p1 gives the fraction of genes in G1 that achieved a score at least as high as h_MPW(gene), if evaluated with the scoring scheme PW_G1G2max(cdn). A p1- value of 0.01 e.g. indicates that 1% of the genes in G1 have a score equal to or greater than h_MPW(gene) if compared to the codon usage of G2_max. The second parameter p2 was derived from a taxonomic rating of those k = 2 or 3 species G2₁-G2_k triggering the k largest score values for gene. The basis for the analysis was a taxonomic tree generated by using material obtained from the ftp-server of the NCBI ftp://ftp.ncbi.nih.gov/pub/taxonomy/. The nodes that represent species belonging to the set CUTG_RF were labelled with an indicator. To calculate the parameter p2, the position of the leaves G2₁... G2_k were used to identify the nearest node (ancestor in the taxonomy tree) t₁ that subsumes the k leaves. If t₁ is the ancestor of those n_t species belonging to CUTG_RF, then the probability p2 of picking by chance k species belonging to the taxonomic group t₁ can be calculated as

Formula (III) was adapted accordingly, if n_t1 was smaller than k. The identification of taxon t₁ and the p₂ value allow to determine the specificity of codon usage. If the high scoring species are taxonomically unrelated, t₁ will be unspecific and p2 relatively large. A specialized codon usage will result in small p₂ values and a more specific taxon.

The concepts introduced so far allowed to characterize individual genes and to quantify related scores statistically. Now, it was necessary to assess the set of all h_max(gene) values in order to derive a cut-off which discriminated those values h(gene) > 0 that deviated significantly from expected fluctuations. Because of the focussing on identifying clusters of CA genes, a statistical approach could be utilized to eliminate false positive predictions. To identify genomic islands and to dynamically adapt the cut-off for each genome individually, a two-pass strategy was used. During the first pass, for each gene with number i, all n_RF scores were determined and h_MPW(gene_i) was identified. A text string genome was created according to the following instruction:

For the string genome the global frequency f_glob(S) was determined and clusters SSSSS indicating a successive sequence of at least five CA genes were localized. These clusters were extended in both directions until the local frequency f_loc(S) fell below the value 2 × f_glob(S). The h_MPW(gene) values of the genes in the extended clusters and the remaining ones were accumulated in two histograms h_cl and h_rem. From the histogram h_cl, the cut-off c_o₂ for round two of the clustering process was derived as the h_MPW value exceeded by 95% of the values determined for genes in extended clusters. c_o₂ allows to estimate the error of not classifying a CA gene correctly: Applying c_o₂ on h_rem gives the number of genes having a score above this cut-off and not being classified as a CA gene. Using cut-off c_o₂, the clustering algorithm was reinitiated and the genes classified as belonging to extended clusters in round two were annotated as being CA. The cut-off for round one was always set to 0.025, a value deduced from the analysis of chromosome two of V. cholerae (see Results).

There were several reasons to design the algorithm as described: The main argument for focusing on clusters was a combination of biological evidence and statistical principles that help to increase the reliability of the prediction. First, it is known that genomic islands frequently have a size of 10 – 200 kb 8. Second, if the probability of annotating a gene as CA is p(S) then the probability for a CA cluster of n successive genes is p(S)ⁿ, if independency is assumed. Thus, for realistic values of p(S) and n it is highly unlikely that such a cluster occurs merely by chance. Even if we consider a large value like p(S) = 0.3, then the probability p(S)⁵ for a cluster of size 5 (as assumed above) is < 2.5 × 10^-3. A rough estimation (1 / p(S)⁵) gives that then one among 400 of such clusters occurs merely by chance and is a false positive classification. This situation allows to gain high sensitivity in identifying individual CA genes and to deliberately adjust the cut-off level as described above. As mentioned, the calculation is based on the assumption that the classification of adjacent genes is independent of the context. Assuming independency is a simplistic model, however a rough approximation, if compared to findings in E. coli: 80% of transcription units (which subsume operons) have less than five genes 46.

The factor 2.0 used in the expression 2 × f_glob(S) for the propagation of extended clusters was inferred from the analysis of the integron island on chromosome two of V. cholerae (see Results). The exact value of this parameter did not critically influence the identification and localization of the integron island (annotation as from 19, data not shown). In general, the algorithm used for the extension of clusters resembles principles implemented in BLAST for the identification of optimal high scoring segment pairs 47.