- Research article
- Open Access
Bootstrap, Bayesian probability and maximum likelihood mapping: exploring new tools for comparative genome analyses
BMC Genomics volume 3, Article number: 4 (2002)
Horizontal gene transfer (HGT) played an important role in shaping microbial genomes. In addition to genes under sporadic selection, HGT also affects housekeeping genes and those involved in information processing, even ribosomal RNA encoding genes. Here we describe tools that provide an assessment and graphic illustration of the mosaic nature of microbial genomes.
We adapted the Maximum Likelihood (ML) mapping to the analyses of all detected quartets of orthologous genes found in four genomes. We have automated the assembly and analyses of these quartets of orthologs given the selection of four genomes. We compared the ML-mapping approach to more rigorous Bayesian probability and Bootstrap mapping techniques. The latter two approaches appear to be more conservative than the ML-mapping approach, but qualitatively all three approaches give equivalent results. All three tools were tested on mitochondrial genomes, which presumably were inherited as a single linkage group.
In some instances of interphylum relationships we find nearly equal numbers of quartets strongly supporting the three possible topologies. In contrast, our analyses of genome quartets containing the cyanobacterium Synechocystis sp. indicate that a large part of the cyanobacterial genome is related to that of low GC Gram positives. Other groups that had been suggested as sister groups to the cyanobacteria contain many fewer genes that group with the Synechocystis orthologs. Interdomain comparisons of genome quartets containing the archaeon Halobacterium sp. revealed that Halobacterium sp. shares more genes with Bacteria that live in the same environment than with Bacteria that are more closely related based on rRNA phylogeny . Many of these genes encode proteins involved in substrate transport and metabolism and in information storage and processing. The performed analyses demonstrate that relationships among prokaryotes cannot be accurately depicted by or inferred from the tree-like evolution of a core of rarely transferred genes; rather prokaryotic genomes are mosaics in which different parts have different evolutionary histories. Probability mapping is a valuable tool to explore the mosaic nature of genomes.
The introduction of small subunit ribosomal RNA as a tool in microbial taxonomy by Carl Woese and George Fox  led most microbiologists to assume that the concepts of animal and plant taxonomy could be extended to the realm of prokaryotes. In particular, it was assumed that a natural taxonomic system for microorganisms was feasible . The goal of a natural taxonomic system is the formation of taxonomic groups that are defined by shared ancestry . By definition, an ancestor that defines a monophyletic group can only give rise to members of this group. No organism outside this group has a lineage that traces back to the same ancestor (paraphyletic group); however, there might be earlier ancestors that define more inclusive monophyletic groups. The metaphor for organismal evolution that underlies a natural taxonomic system is a strictly bifurcating tree of species. A decade ago ribosomal RNA promised that one day it might be possible to place every extant organism on a universal tree of life, and the hope was that more genomic sequences would make this placement more accurate.
However, the analyses of completely sequenced genomes initiated a reassessment of concepts in microbial evolution . While some molecular markers were found to agree with one another e.g., , others do not [6–12]. Transfer of genetic information between divergent organisms has turned the tree of life into a net or web , and genomes into mosaics. Different parts of genomes have different histories, and representing the history of genome evolution as a single tree appears inconsistent with the data. Nevertheless, the assumption of a tree-like process still underlies many approaches. Genome content trees have been calculated based on the presence and absence of genes [14–16] or types of protein folds . While there is limited agreement between genome and rRNA phylogeny, at present it remains unclear whether this similarity is based on shared ancestry of part of a less frequently exchanging genome core , or if the apparent congruence is itself the result of horizontal gene transfer .
Overall genome content is not best represented on a single tree. Fig. 1 gives an example of an alternative depiction, where thickness of a line reflects percentage of genes shared between two genomes. The coherence among the three domains of life (Bacteria, Archaea, Eucarya ), is clearly reflected in genome content; i.e., Archaea share more genes with other Archaea than with Bacteria, but many features are incompatible with representing the relationships between different genomes as a tree. For example, the mesophilic euryarchaeon Halobacterium sp. has more genes in common with the mesophilic Bacteria than does the thermophilic crenarchaeote Aeropyrum pernix. However, the extremophilic euryarcheote Archaeoglobus fulgidus shares many more genes with the extremophilic bacteria, Aquifex aeolicus and Thermotoga maritima than does Halobacterium. While this example illustrates the web-like relationships among genomes, recent phylogenetic reconstructions from molecular data have explored only few alternatives to the tree-paradigm (e.g. [21, 22]).
One obvious drawback of the star-like representation in Fig. 1 is that it utilizes BLAST search results only. Any phylogenetic information retained in the sequences is not utilized beyond the presence or absence decision based on a single expectation value cut-off. Because of recombination, individual genes themselves might be mosaic ; however, within-gene recombination of protein coding genes occurs mostly between closely related organisms. The redundancy of the genetic code greatly reduces recombination between divergent proteins. Even if a region is 100% conserved on the amino acid level, the encoding DNA can be so different as to allow the mismatch repair system to prevent recombination. For studies of single divergent orthologous protein encoding genes the assumption of a tree-like evolutionary history remains a reasonable expectation. In this manuscript we focus on methods that utilize the phylogenetic information that is retained in molecular sequence data, while not presuming that genomes as a whole evolved in a tree-like fashion.
In an elegant approach Korbinian Strimmer and Arndt von Haeseler  utilized Bayesian posterior probabilities to assess the phylogenetic information contained in an alignment of four homologous sequences. With four sequences there are only three possible tree topologies, and thus the three posterior probabilities corresponding to these three trees must sum up to one. Utilizing a barycentric coordinate system, the resulting probability vector is represented as a point in an equilateral triangle (Fig. 2), where the distances of the point P to the three sides represent the three probabilities. Strimmer and von Haeseler applied this approach to depict the phylogenetic information content present in a multiple sequence alignment. They plot the results from the analyses of all possible quartets, where the four sequences are selected from a single multiple sequence alignment in the same coordinate system. If there is a lot of phylogenetic information in the alignment, then most probability vectors will fall close to one of the corners; conversely datasets containing little phylogenetic information will mainly result in vectors falling into the center of the triangle. Here we explore the application of this and similar approaches in comparative genome analyses. In particular, we compare different approaches to calculate Bayesian posterior probabilities, and we compare these probabilities to the more widely used bootstrap support values. We assess the reliability of the different probability mapping approaches through their application to mitochondrial genomes, and we illustrate their usefulness by mapping selected interphylum and interdomain relationships.
Results and Discussion
Overview of data flow in probability mapping
An outline of our approach to genome probability mapping is given in Figure 3. Using SEALS  and MySQL we developed scripts that identify and retrieve quartets of orthologous protein-encoding open reading frames (QuartOPs) from four selected genomes. We use the term genome to denote the collection of all ORFs identified in a genome. (In the case of genomes that are not well annotated, it is feasible to use a very wide definition of ORF, e.g, all amino acid sequences encoded between two stop codons in any of the six possible reading frames. As long as one of the genomes included in the analyses is properly annotated, only those identified ORFs that are actually homologous to an identified ORF will become part of a quartet of orthologs.) We utilize an operational definition of an ortholog: two open reading frames are considered orthologous, if and only if they are each other's top scoring BLAST hit when one is used as a query to search the other genome. A QuartOP is formed when each of the open reading frames picks the other members of the quartet as the top scoring hit in searches of the respective genomes. QuartOPs are similar to the clusters of orthologous groups (COGs) maintained by the NCBI [26–28], but differ in that COGs require only unidirectional, circular best hit relationships for three of the reference genomes, whereas we require the reciprocal top hit relationship for the four genomes included in a quartet, and we do not limit our identification of QuartOPs to a number of reference genomes. Montague and Hutchison utilized a comparable approach in their definition of congruent COGs . So far we have analyzed 68 genome quartets (see supplementary material). The number of QuartOPs identified per genome quartet ranges from 82 (for genome quartet #6: Deinococcus radiodurans, Treponema pallidum, Escherichia coli, and Halobacterium sp.) to 1182 (for genome quartet #63: Agrobacterium tumifaciens, Sinorhizobium meliloti, Mezorhizobium loti and Caulobacter crescentus).
Each of the aligned QuartOPs from a genome quartet was analyzed with respect to the posterior probability of the three possible tree topologies given the aligned QuartOP. Routinely we calculated these probabilities using Strimmer's and von Haeseler's approach : Using each of the three topologies as a usertree, we calculated the maximum likelihood for each of the three topologies given the data. We then use the three maximum likelihoods to calculate the probability for topology i according to the formula: P i = L i /(L1+L2+L3), where L i is the likelihood for the best tree given topology i. Other types of reliability measures used to evaluate QuartOPs were bootstrap support values and Bayesian posterior probabilities estimated using MrBayes program (see below).
An example for the comparison of four genomes from different phyla is given in Fig. 4A. Surprisingly, each of the three tree topologies is strongly supported by more than 40 QuartOPs, and most of the QuartOPs appear to strongly support one of the trees. None of the three possibilities has majority support. Figure 5 lists the functional categories of those QuartOPs that strongly support the different tree topologies. None of the categories shows a preference for a particular tree topology. For each tree topology more than 50% of the strongly supporting QuartOPs belong to the category "information storage and processing", while this category contains only about 1/3 of the genes present in the genomes. While the genes in this category appear more conserved and phylogenetically informative, the strong support that the genes in this category provide is nearly evenly split between the three possibilities.
Impact of model parameters and sequence conservation
To test if ill-aligned sequences might have had an impact on the analyses, we repeated the analysis of genome quartet # 8 (see Figure 4) using only QuartOPs that contained very similar sequences. By default we only excluded top hits with an E-value larger than 10-4. We repeated the example given in Fig. 4A with a cut-off of 10-20, i.e., we not only required the sequences in a QuartOP to be each others top hit, but in addition we asked for a high similarity between the two sequences. As a result the support for the three topologies in genome quartet #8 dropped to 54 (44, 38), 51 (45, 32), 39 (29, 28) (the numbers in parenthesis are the numbers of quartets that support the topology with posterior probability larger than 90% and 99%, respectively). To access the level of sequence conservation within the QuartOPs' sequences, we calculated the average percentage of pairwise identity per QuartOP. It varied from 40.53 10.54% to 43.84 ± 9.7% when the E-value cut-off was varied between 10-2 and 10-20 (see supplementary material for the summary table). While pairwise sequence identity is not a universally dependable measure of phylogenetic information content, these values illustrates that the sequences within a QuartOP are neither identical to one another, nor so divergent as to be saturated with substitutions and of questionable homology . Using only the most conserved QuartOPs does not change the qualitative result: each of the three possible tree topologies is supported by about an equal number of QuartOPs (see supplementary material).
We recalculated the likelihoods for all QuartOPs in genome quartet #8 using a model that incorporates among site rate variation (ASRV). The posterior probabilities calculated according to Strimmer and von Haeseler did not change dramatically and each of the three tree topologies is still supported by roughly equal number of QuartOPs. The maps for this analysis are available in the supplementary material.
Estimating Bayesian Posterior Probabilities
The formula used by Strimmer and von Haeseler  to calculate posterior probabilities (i.e. the probability that tree topology T i is true given an aligned set of four sequences) considers only three trees (i.e. branch lengths and topology), each with the same prior probability. These three trees are those that have the highest likelihood for the three possible topologies. However, there are infinitely many other trees that differ from the three chosen ones only by differences in branch lengths. What is the effect on the calculated posterior probability of using only the single best tree as a representative of all the trees with the same topology? There is no a priori reason to exclude the other trees that have slightly lower likelihoods.
A different approach that does not make these assumptions is the use of Markov Chain Monte Carlo methods to explore tree space. We used the program MrBayes written by Huelsenbeck and Ronquist . Using a QuartOP with posterior probabilities of .76, .10 and .13 we explored different parameter choices for the biased random walk through tree-space. We chose two chains with 5,000 burn-in cycles, and 25,000 cycles with sampling after every cycle as a compromise between increased precision of the probability estimate and computation time (see Materials and Methods for more details).
The result of calculating the posterior probabilities of all QuartOPs in genome quartet #8 is given in figure 4B. Again all of the three tree topologies are strongly supported by some QuartOPs. When we repeated this analysis using the same settings, none of the probabilities changed by more than a few percent. The support for the three tree topologies changed from 67/47/37, 69/40/22 and 86/55/32 (the three numbers indicate total support and QuartOPs that supported a topology with more than .90 and .99 respectively) in the first run to 67/47/37, 70/41/22 and 85/55/32 in the second, indicating that the chosen parameters provided satisfactory reproducibility. Plots of both analyses are available in the supplementary material. Comparing figure 4B with 4A it is clear that in this case the Bayesian posterior probabilities estimated with MrBayes are more conservative assessments of reliability than the ones calculated according to . The 99% support level calculated according to  approximately corresponds to the 90% support level calculated with MrBayes.
Bootstrap support values versus posterior probabilities
To facilitate comparison of Bayesian posterior probabilities with a more widely used confidence measure, we generated 100 bootstrapped samples  from each QuartOP in case #8. Each of the bootstrapped samples was analyzed using maximum likelihood with the same model of substitution as before. Each of the bootstrapped samples supports one of the three possible topologies, thus the sum of the bootstrap support values for the three topologies adds up to 100%, and the percentage of bootstrapped samples for each QuartOP that best supported each tree was again plotted in a barycentric coordinate system (Fig. 4C). Many more QuartOPs map into the central region of the triangle as compared to Figure 4A and 4B. Clearly, for this test bootstrap support values are more conservative measures of support than either of the posterior probabilities calculated above. Nevertheless, there are still several QuartOPs that strongly support each of the three tree topologies; however, there are 22 QuartOPs that support grouping E. coli with Treponema pallidum with better than 90% bootstrap support, whereas the alternatives are supported by only 12 and 13 QuartOPs, respectively. Comparing Figures 4A and 4C it appears that in analyzing quartets 70% bootstrap support is comparable to .99 posterior probability calculated according to .
Comparison of the different reliability assessment tools
ML-mapping according to  is the least conservative of the tools explored. For the test cases analyzed a posterior probability of .99 according to , corresponds to a Bayesian posterior probability of .90 calculating using a Markov chain exploration of tree-space using  and about 70% bootstrap support. We did not find a strong dependence of the results on the substitution models used in calculating likelihoods and separate runs indicated satisfactory precision of the calculated probabilities and bootstrap values. Given that we only analyzed about 300 QuartOPs using all three approaches it would be premature to generalize our findings; however, other analyses that utilized both bootstrapping and Bayesian posterior probabilities also found bootstrapping to be more conservative than posterior probabilities calculated using Bayesian methods with Markov chain Monte Carlo sampling (e.g., [33–35]).
While gene transfer into the mitochondrial genomes has been inferred [36–39], mitochondrial genomes are expected to have undergone many fewer legitimate and illegitimate recombination events than free-living prokaryotes. Clearly, if probability mapping is to be considered a reliable approach, we expect that when analyzing quartets of mitochondrial genomes, the different genes should all support the same tree topology.
In most instances, this expectation is fulfilled (see Table 1), even though we selected instances in which the splits could be expected to be ill resolved, e.g., echinoderm, mammal, insect, mollusk (m4), or protist, fungus, animal, plant (m7). The only exception was an ORF in quartet m7 that encodes the cytochrome oxidase subunit II. This ORF did not support grouping the animal with the fungal homolog as expected; rather it grouped the protist and animal homologs together (posterior probability according to  was » 0.99). Inspection of the aligned sequences (Fig. 6) revealed that there are more residues shared between the homologs from Cafeteria roenbergensis and Homo sapiens thanbetween the homologs from Cafeteria roenbergensis and Arabidopsis thaliana. No artifact that could be responsible for this unexpected grouping was detected. The same high support for this unexpected grouping is also recovered in bootstrap analysis and in posterior probabilities calculated with MrBayes .
The finding of a QuartOP in a mitochondrial genome quartet that supports a non-traditional grouping could either reflect a rare recombination event, selection pressures that led to convergent evolution in two lineages, or a chance event – if one looks at enough samples one will find some that (considered by themselves) appear significant. At present it is not possible to decide between these three possible explanations. Our analysis of mitochondrial genomes shows that in most instances the calculated probabilities (ML-mapping, Bayesian posterior probabilities, or bootstrap values) support the expected tree topologies, albeit with surprisingly strong support values. Rarely, unexpected groupings can be recovered and support for these probably erroneous groupings can be high. In most instances the ML-mapping approach accurately revealed the expected relationships between the mitochondrial genomes. This confirms the suitability of this approach in genome analyses.
Interphylum genome quartets
Here we focus on examples that illustrate the utility of the probability mapping approach. Focusing on the relationships between the cyanobacteria with other bacterial phyla we calculated several genome quartets that include the Synechocystis sp. genome and three members each of other bacterial phyla (see Table 2). In all cases that included both Bacillus subtilis as a representative of the low GC Gram positives, and Synechocystis sp., the majority of QuartOPs supported the topologies that grouped these two organisms together. The alternative topologies were significantly supported by some QuartOPs, but the number of strongly supporting QuartOPs was lower than for the B. subtilis – Synechocystis grouping. This also was true when one of the other two genomes was from a high GC Gram positive (genome quartets #53, #54, #55 and #68). Only when two low GC Gram positives were included in the same quartet, was the intra-phylum grouping of low GC Gram positives supported by many more QuartOPs than the grouping of B. subtilis with Synechocystis sp. (genome quartets #51 and #52).
Previous analyses based on a limited number of proteins and signature insertions and deletions had suggested different bacterial groups as closest relatives to cyanobacteria. Among the suggested sister groups were the Deinococcales  and spirochetes [41, 42]. Our analyses do not support these earlier claims, but are in agreement with the recent analyses of genes involved in chlorophyll biosynthesis , which indicated that the low GC Gram positive heliobacteria are closest to the last common ancestor of all oxygenic photosynthetic lineages. The analyses summarized in Table 2 also illustrate that interphylum HGT, while turning genomes into mosaics, has not eroded all associations between bacterial phyla. In the case of cyanobacteria, a close association between low GC Gram positives and the cyanobacteria is supported by the majority of conserved genes. Similar observations of reproducible associations between phyla based on genome wide comparisons were recently published [44–47]. However, at present it cannot be decided to what extent these closer associations reflects shared ancestry or are due to preferred HGT .
Interdomain genome quartets
In our search for the "sister-phylum" to the cyanobacteria we also analyzed a few quartets including Archaea. One noteworthy finding was that in the genome quartet including Synechocystis sp., Halobacterium sp., Aquifex aeolicus and Thermotoga maritima the grouping of Halobacterium sp. with Synechocystis sp. was recovered by many more QuartOPs (56 with p > .99) than the grouping that would be expected following 16S rRNA phylogeny (12 QuartOPs with p > .99; see Table 3). To test if this association was specific for Synechocystis sp., we repeated the analyses replacing Synechocystis sp. with Bacillus subtilis. The result was qualitatively the same: at the p > .99 level 53 QuartOPs supported grouping Bacillus subtilis with Halobacterium sp., and only 27 supported grouping Aquifex aeolicus with Halobacterium sp. (Fig. 7).
Clearly, there are many artifacts possible in analyzing divergent sequences. For many QuartOPs the ortholog from Halobacterium sp. is expected to be the longest branch. To test for the possibility that long branch attraction  might be the reason for the strong support of Halobacterium sp. grouping with Synechocystis sp., we repeated the analysis replacing the Halobacterium sp. genome with that from Archaeoglobus fulgidus, another archaeon. Gratifyingly, many more QuartOPs supported the grouping of the thermophilic archaeon Archaeoglobus with the thermophilic bacteria Aquifex and Thermotoga. The different interdomain genome quartets that include a meso- or thermophilic archaeon are summarized in Table 3.
An analysis of the putative functional assignments of the QuartOPs that grouped Halobacterium sp. with the mesophilic bacteria is given in Table 4. To assess which of these categories have an increased percentage of QuartOPs as compared to distribution of ORFs within the genome, we also calculated the distributions of ORFs among functional categories in the Halobacterium sp. and A. fulgidus genomes. Open reading frames within a genome are distributed almost evenly among the four meta-categories (see columns labeled "H" and "A"). However, the QuartOPs that group the halobacterial orthologs with those from mesophilic Bacteria are distributed differentially among the meta-categories. Most of the QuartOPs are in the "Metabolism" and "Information Storage and Processing" meta-categories. These are also the categories in which Halobacterium sp. shows many more OuartOPs in support of topology 3 than A. fulgidus.
The analyses described in this section reconfirm that genes have been transferred across domain boundaries [6–12]. Not surprisingly, these transfers appear to occur preferentially between organisms living in the same or similar environment. The genome of the mesophilic Halobacterium sp. contains many genes that group with the orthologs from mesophilic bacteria, whereas the majority of genes from the thermophilic archaeon Archaeoglobus fulgidus group with the orthologs from the extremely thermophilic bacteria. The majority of QuartOPs that group the halobacterial orthologs with the ortholog from the mesophilic bactria belong to two of four meta-categories: "Information Storage and Processing" and "Metabolism". QuartOPs in Information Storage and Processing meta-category that support the grouping of Halobacterium sp. with Synechocystis/Bacillus are listed in the Table 5. A complete listing is available in the supplementary material. As expected, this list includes several tRNA synthetases, which were previously found to be frequently transferred [6–8], and enzymes involved in DNA repair (cf. ). More surprisingly, this list also includes translation initiation factors and several ribosomal proteins. The latter were assumed to be infrequently transferred, but recent analyses reported them to be horizontally transferred among bacterial lineages [10, 11]. The initiation factor IF-2 in Halobacterium sp. was previously shown to have strong similarity to the initiation factor IF-2 from Bacteria . Most of the genes that group Halobacterium with the mesophilic bacteria encode functions that were postulated to be frequently exchanged . While no meta-category appears exempt from HGT, some functions appear to be more often transferred than others (cf. Table 4).
Maximum likelihood mapping is a useful tool for analyzing and depicting the mosaic nature of genomes. ML-mapping is much less conservative than other approaches of estimating Bayesian posterior probabilities. If ML-mapping is used as the only probability mapping tool, the overestimation of supporting probabilities has to be taken into consideration. A posterior probability of .99 calculated with ML-mapping often corresponds to a posterior probability of only .90.
Many relationships among prokaryotes cannot be depicted by a tree-like pattern reflecting a core of rarely transferred genes. Rather prokaryotic genomes are mosaics where different parts have different evolutionary histories. However, HGT between divergent organisms has not erased all patterns of interphylum relationship. For example, the majority of QuartOPs group the cyanobacteria with the low GC Gram positives as sister phyla.
Due to horizontal gene transfer even organisms from different domains living in the same or similar environments share more genes with each other than organisms with a similar degree of divergence that live in different environments. These interdomain horizontal transfers mainly concern proteins involved in nucleotide, carbohydrate and amino acid transport and metabolism; however, proteins that are part of the translation machinery or are involved in DNA repair appear to be transferred across domain boundaries as well.
Materials and Methods
Completed genomes were retrieved from the NCBI's FTP site ftp://ncbi.nlm.nih.gov/genbank/genomes/ in the form of amino acid sequences encoded by open reading frames (ORFs) as identified in the annotated genomes. Mitochondrial genomes were obtained from the Organelle Genomes Page at NCBI http://www.ncbi.nlm.nih.gov/PMGifs/Genomes/euk_o.html. The genomes were formatted using the formatdb program from the stand-alone BLAST package, initially of version 2.0.11 and later of versions 2.1.2 and 2.2.1 as they were released . All analyses were performed locally.
Data Flow in Quartet Analyses
For each set of four genomes, BLAST [51, 52] searches of every ORF in one genome against the other three genomes were performed using the blastp program. The E-value cutoff for the BLAST searches was set to 10-4 (in one test case an E-value cutoff of 10-20 was used). For every BLAST search the GI number of the top hit (if it was below the cutoff) was saved along with the GI number of the query sequence forming a GI pair. This resulted in twelve lists of GI pairs for each of the twelve possible pairwise genome comparisons. This information was further used to identify quartets of orthologous proteins (QuartOPs). Following Tatusov et al.  we defined QuartOPs as those sets of genes that mutually pick each other as the top scoring hit in the BLAST comparisons. The detection of the QuartOPs was performed using the MySQL database software http://www.mysql.com. The lists of GI pairs were entered into twelve tables of a database. The tables were joined into one table under conditions that satisfy the definition of the QuartOPs (see above). This resulted in a table with four columns of GI numbers for QuartOPs. The amino acid sequences for each QuartOP were retrieved from GenBank at NCBI and were aligned using ClustalW 1.8 . QuartOPs were analyzed using the ML-mapping approach according to Strimmer and von Haeseler, Bayesian probabilities mapping and bootstrap support values mapping techniques (see details below).
Posterior probabilities according to Strimmer and von Haeseler
For all three possible unrooted tree topologies maximum-likelihood values and posterior probabilities were calculated using in-house JAVA programs that were written utilizing classes from the Phylogenetic Analysis Library version 1.0  and parts of Vanilla package version 1.0 . If not indicated otherwise, likelihood values were estimated using the automatically selected suitable substitution model (chosen from BLOSUM62, CPREV, Dayhoff, JTT, MTREV24, VT and WAG) with no ASRV. The maximum-likelihood mapping approach was further used to visualize support for each tree topology , i.e. the posterior probability vector for each QuartOP was plotted into an equilateral triangle. Maximum-likelihood maps were generated using GNUPlot v. 3.7 http://www.gnuplot.info/.
Posterior Probabilities calculated with MrBayes program
Posterior probabilities were also calculated with MrBayes version 2.01 . Each QuartOP was analyzed with two simultaneous Markov chains for 25,000 cycles under the JTT substitution model  without ASRV. One chain was heated with the temperature set equal to the default value of 0.2. Samples were taken at each cycle. The "burn in" option was set to 5,000 cycles. The remaining 20,000 cycles were used to calculate posterior probabilities for each of the three tree topologies. The posterior probabilities were plotted to equilateral triangle as described above. For discussion of the choice of the parameters see below.
Bootstrap Support Values
As an alternative to posterior probability vectors, bootstrap support values were calculated and plotted. Each QuartOP was bootstrapped 100 times and the proportion of bootstrapped datasets supporting each tree topology was recorded as a bootstrap probability vector. The bootstrap probability vectors were plotted into an equilateral triangle with the zones changed to "total", "70%" and "90%" (see Fig. 2).
Empirical Search for Optimal MrBayes Parameters
To find parameters that will return consistent posterior probabilities within reasonable computation time, one QuartOP from mitochondrial genome quartet #m1 was analyzed multiple times with different parameters. According to Strimmer and von Haeseler's approach  this QuartOP has posterior probabilities of 0.76, 0.10 and 0.13. In all runs samples were taken at each cycle; two chains and the JTT substitution model  without ASRV were used.
First, we analyzed the dataset with 250,000 cycles. We tried different "burn in" options in the range of 1,000–20,000. The posterior probability values changed by less than 0.3% from case to case. We selected a "burn in" of 5,000 cycles in further analyses. Second, we tried different numbers of cycles to calculate posterior probabilities. The probabilities were calculated using 10,000–240,000 cycles with increment of 10,000 cycles. Again, the posterior probability values did not change significantly from case to case. Third, we raised the "temperature" parameter T to 2.0 for the second, heated chain. This did not result in changes of the estimated posterior probabilities. Fourth, we used 25,000 cycles and repeated the analysis 10 times, calculating average and standard deviation of all runs. For all three probabilities the standard deviation was less than 0.01. Based on these analyses we selected 25,000 cycles with a "burn in" of 5,000 as a compromise between precision of probability estimation and computational time spent. As a final test, we performed the analysis of the quartet #8 twice with selected parameters. This did not result in significantly different maps. Graphs and tables depicting the results of these analyses are given in the supplementary material.
Mapping taking ASRV into account
For the genome quartet #8 we calculated posterior probabilities under the model which takes ASRV into account with Strimmer and von Haeseler's  approach and with the MrBayes program version 2.01 . TREE-PUZZLE 5.0  was used to calculate posterior probabilities according to Strimmer and von Haeseler . A discrete approximation of the gamma distribution  was used to describe ASRV. Eight rate categories were used in TREE-PUZZLE , and four rate categories were used in MrBayes . The maps are available in the supplementary material. Due to the amount of time required for calculations, the analyses were not performed for other genome quartets.
Functional assignments using the COG database
Datasets for QuartOPs with strong preference for a particular tree topology (i.e. with posterior probability above 99% for that particular topology, or in other words the QuartOPs located in the very corners of the equilateral triangle) were extracted. For each of those QuartOPs the COG functional category  was identified. In order to detect the functional categories, the COG database was downloaded from NCBI's FTP site (initially the year 2000 release and later the year 2001 release). The COG database was formatted using the formatdb program of BLAST package. Every QuartOP was compared to the COG database using the blastp program. The category of the each sequence in the QuartOP was assigned according to the category of the top hit of each BLAST search. The numbers of QuartOPs in each functional category were calculated for each of the three tree topologies.
Distribution of ORFs among COG categories for complete genomes of Halobacterium sp. and Archaeoglobus fulgidus
Every predicted ORF in a genome was compared to the COG database (release of year 2001) using the blastp program with E-value cutoff 10-4. The category of each ORF was set to be equal to the category of the top hit of the corresponding BLAST search. Category Q was dropped from the results, because the corresponding genome quartets were analyzed with the previous release of the COG database (release of year 2000) that did not contain the Q category.
Data Analysis Automation
The repetitive tasks of analyses were automated using the SEALS package version 0.824 . The tasks that were not available through SEALS package were programmed in PERL v. 5.005. The PERL scripts and JAVA programs are available upon request.
Mitochondrial Genome Quartets Analyses
Seven mitochondrial genome quartets were used as controls and were analyzed with the three approaches for genome quartet analysis described above. For calculation of posterior probabilities with MrBayes at least 25,000 cycles were used.
Supplementary material is located at the QuartOP web page http://carrot.mcb.uconn.edu/quartets/. This web page includes the summary of all genome quartets analyzed (with maps), the results of control analyses, and a form to request the scripts described in this article. ML maps are available in postscript and PDF formats. An offline version of the QuartOP web page is available as a compressed archive named supp_material.zip and as a self-extracting archive supp_material.exe for Microsoft Windows users. The archive can be expanded using WinZip http://www.winzip.com/ for Windows, StuffIt for Macintosh http://www.stuffit.com/, or unzip utility for Unix. The uncompress utilities have to be run with the option to preserve the subdirectory structure inside the archive. To access the information in the archive, the file index.html has to be opened using an Internet browser. This index.html file is located in the root directory named "offline_quartops". All the files in the archive are hyperlinked and accessible through the index.html file.
horizontal gene transfer
cluster of orthologous groups
ribosomal ribonucleic acid
Basic Local Alignment Search Tool
quartet of orthologous proteins
System for Easy Analysis of Lots of Sequences
National Center for Biotechnology Information
Among Site Rate Variation
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We thank Paul Lewis and Lorraine Olendzenski for many stimulating discussions and for critically reading the manuscript. The work was supported through the NASA Exobiology Program and through the NASA Astrobiology Institute at Arizona State University.
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Zhaxybayeva, O., Gogarten, J. Bootstrap, Bayesian probability and maximum likelihood mapping: exploring new tools for comparative genome analyses. BMC Genomics 3, 4 (2002). https://doi.org/10.1186/1471-2164-3-4
- Posterior Probability
- Mitochondrial Genome
- Bootstrap Support
- Tree Topology
- Bayesian Posterior Probability