Gene insertions and deletions can be inferred by examining the presence or absence of a gene (or a gene family) on a phylogenetic tree. In some recent studies, the parsimony method has been used to infer insertions/deletions (Daubin et al. 2003a, b; Mirkin et al. 2003; Hao and Golding 2004). Gene insertions have been distinguished as gene genesis (birth) or lateral gene transfers (LGT), and insertions/deletions have been tested with varying penalties for LGTs in different methodologies (Snel et al. 2002; Kunin and Ouzounis 2003; McLysaght et al. 2003). However, the inference of insertions/deletions is difficult because of the possibility of parallel deletions and insertions on multiple branches (Copley and Dhillon 2002; Snel et al. 2002; Stoebel 2005) and because of variable evolutionary rates of change on different branches (Hao and Golding 2004). Furthermore, the parsimony method is well known to underestimate the number of events in phylogeny reconstruction (Galtier and Boursot 2000; Dean et al. 2002; Felsenstein 2004).

Likelihood analysis has been successfully used to reconstruct phylogenies using sequence data since its first application by Neyman (Neyman 1971; Felsenstein 1988, 1989, 2004; Gu 2001). Maximum likelihood analyses have also been applied to the study of genome content (Gu and Zhang 2004; Huson and Steel 2004), and the phyletic pattern of gene presence/absence has been used to reconstruct evolutionary history in a Markov analysis (Lake and Rivera 2004). In this study, a maximum likelihood method is used to infer insertion/deletion rates on the phylogeny of the Bacillaceae group of Gram-positive bacteria. An advantage of this group is the large number of genomes that have been completely sequenced.

The strains from Bacillus anthracis, Bacillus cereus, and Bacillus thuringiensis are closely related and have been suggested to form the B. cereus group (the Bc group) (Priest et al. 2004). Two different insertion/deletion rates were assumed on the two parts of the phylogeny (Case 2 in Fig. Fig.2).2). The branches among the Bc group have an insertion/deletion rate α, while the remaining branches have an insertion/deletion rate β. Fitting the maximum likelihood model to this scenario suggests that the rate α is 4.42, while the rate β is 0.35 (Fig. (Fig.3).3). It is striking that the rate α is much greater than the rate β and also much larger than 1, which is the evolutionary time period required to observe one substitution per nucleotide site. Hence, during the evolutionary time period required for one substitution per site, an entire gene could possibly have been inserted/deleted about five times in the Bc group. There are more gene movements observed relative to evolutionary branch length by comparing more closely related strains, and hence, there are more gene movements inferred at the tips of phylogeny.

As can be observed in Figure Figure2,2, there is a divergence in the genome size between the Bc group and the genome size of the other Bacillaceae. The branch leading to the Bc group was therefore separated from the other branches with a distinct rate γ (Case 3 in Fig. Fig.2).2). The application of the maximum likelihood analysis to this model indicates that the rate α is 3.92, the rate β is 0.28, and the rate γ is 1.23. The rate γ is approximately five times greater than the rate β. However, the rate α among the Bc group measuring rates closer to the tips of the phylogeny is still much greater than either the rate β or γ.

In addition to the above likelihood analysis, an analysis was performed with the assumption that genes cannot be regained after having been deleted. These results yield insertion/deletion rates that are similar to those under the assumption that genes can be regained after deletion (Table 2). However, in every case, the likelihood value is much lower. With a single constant insertion/deletion rate, the MLE is 0.48. In the case of two separate rates, the rate α is 4.48 among the Bc group and the rate β is 0.33. When the rate on the branch leading to the Bc group was also considered distinct, the rate γ was estimated at 1.08 and the rate β as 0.28. Both rates β and γ are much smaller than the rate α at 3.90.

Finally, the rate on internal branches in the Bc group was separated from that on external branches in the likelihood estimation (boxed portion of the phylogeny in Fig. Fig.2).2). This shows that the insertion/deletion rate on external branches is higher than that on internal branches under both models of gene transfer (4.42 vs. 3.62 and 5.34 vs. 2.78, respectively) (Table 3). If the branch leading to the three B. anthracis strains is treated as an external branch in the likelihood estimation because of the close evolutionary relationship of the B. anthracis strains, the rate difference between external branches and internal branches becomes more dramatic (7.19 vs. 0.91 and 7.63 vs. 0.81, respectively) (Table 3). This again confirms that more gene insertions/deletions take place at the tips of the phylogeny.

To explore among the most closely related taxa, five strains from the Bc group; B. anthracis Ames (Ba₁), B. anthracis Ames “ancestor” (Ba₂), B. anthracis Sterne (Ba₃), B. thuringiensis (Bt), and B. cereus ZK (Bc₁) were analyzed separately. The comparison of homologs shows that >96% of the genes present in all five strains share at least 90% sequence identity with each other in their protein sequences. Therefore, the substitutions between homologs among these five strains should be considered as relatively limited. All phyletic patterns of these five strains are shown in Table 4. Of the 5076 gene families, there are only 3956 present in all five strains. Hence, 22.1% of the genes are not shared by all five strains, even though these five strains are believed to represent one species (Helgason et al. 2000) and to have diverged very recently.

To determine the rates of evolution in the recently transferred genes, the tree lengths for the Bc-group-specific genes were measured (Fig. (Fig.4A)4A) and compared with the tree lengths of genes present in all 13 strains (Fig. (Fig.4B).4B). In both cases, only the branch lengths within the Bc group of taxa were measured. This comparison indicates that the genes that are strain specific within the Bc group have much faster rates of evolution than do more ancestral genes present in the other taxa.

The results demonstrate that LGT occurs rapidly and extensively between strains of the same species. A phylogeny was constructed to measure the rate of LGT relative to nucleotide substitutions. The concatenated DNA sequences of gmk, glpF, and pycA genes rather than ribosomal RNA sequences were used to reconstruct the phylogeny in this study. It is difficult to reconstruct the phylogenetic relationship within the Bc group owing to their remarkably similar rRNA sequences (Ash et al. 1991) and the divergence of rRNA sequences in genomes with multiple rrn operons (Klappenbach et al. 2001; Acinas et al. 2004). The gmk, glpF, pycA, tpi, ilvD, pta, and pur genes have been studied in the past as tools for reconstructing the evolutionary history of the B. cereus group. It was found that gmk, glpF, pycA, and tpi genes strongly conform to the concatenated tree of all seven genes (Priest et al. 2004). (Note that the topological position of Oceanobacillus iheyensis in the concatenated phylogeny is different from that in a 16S rRNA-based phylogeny [Hao and Golding 2004].)

When maximum likelihood estimates of the rates of insertion/deletion are mapped onto this phylogeny, it suggests that there are more genes coming in and going out at the tips of phylogeny. This is clear even if one looks at the table of gene presence/absence (Table 1) and observes that differences in gene content between taxa that are considered a single species are among the most common patterns observed. If this is an evolutionarily stable situation, then most of the laterally transferred genes must be lost shortly after their insertion during evolution. Genome annotation can be an error-prone task (Kyrpides and Ouzounis 1999). As a result, all of the predicted ORFs that are present in only one genome and that do not have homologs detectable by BLAST were removed from this study. Since many of these may be proper and functional genes (Siew and Fischer 2003, 2004), this method tends to further underestimate the events on external branches. Not surprisingly, a maximum likelihood estimation including the uniquely present ORFs further inflates the rates at the tips of phylogeny (data not shown).

It has been suggested that B. anthracis, B. cereus, and B. thuringiensis are one species (Helgason et al. 2000). A close evolutionary relationship among these strains is inferred by comparing substitutions in the concatenated sequences (Fig. (Fig.1)1) and from the protein similarity among five of the most closely related members from the Bc group. On the other hand, >22% of the genes are not present in all five strains (Table 4). Together this shows that gene insertions/deletions have a role in the evolution of these strains equal to or greater than the role of changes at the sequence level. This compares favorably to the results of Lynch and Conery (2003) that the rate of gene duplications is also of the same order of magnitude as base substitutions. The maximum likelihood analysis within the Bc group was performed by optimizing separate insertion/deletion rates on internal branches and external branches. It shows that the tips of the phylogeny have greater insertion/deletion rates (Table 3). Nor can the high insertion/deletion rates in these genomes be simply explained by a highly mobile feature of genomes such as pathogenicity islands. Although three pathogenicity/genomic islands have been reported in B. cereus ATCC 14,579 (Bc₃) in a previous study (Zhang and Zhang 2003), most of the annotated ORFs in these islands have been excluded from this study since they do not have homologs in completed genomes from other bacteria. Additionally, while the Bc₃ strain-specific genes in this study are not located in these three islands, they too are excluded as they lack known homologs in other species. It is plausible that the ORFs in the strain-specific pathogenicity islands, if they are real genes and not annotation errors or pseudogenes, might contribute to an even higher turnover rate than that found in this study. Indeed, it has been shown that islands can have high numbers of insertions, deletions, and pseudogenes (Ullrich et al. 2005). High rates on external branches are observed in this study, and therefore, the addition of strain-specific genes or unique genes on pathogenicity islands would further inflate the rate at the tips of phylogeny.

In the maximum likelihood estimation, the insertion rate is assumed to be equal to the deletion rate. This assumption was made to ensure that in the long term, genome sizes would not tend to zero or infinity. In the short term, this assumption is unlikely to be correct, and Thompson et al. (2005) have shown that even within closely related bacterial populations, the genome content may change. The model of gene insertion/deletion can be improved by assuming unequal rates of insertion/deletion, fixed numbers of genes that are not deleted, variation in indel rate among genes, and so on. But the increased rate at the tips of the phylogeny is not likely to be an artifact of genome size variation or the limitations of the likelihood model. Firstly, the members of the Bc group have larger genome size than the non-Bc group taxa, but, while the indel rate on the branch leading to the Bc group shows a higher rate, it is still much smaller than the rate within the Bc group. Secondly, the seven members of the Bc group have similar genome sizes, and an estimation using only the members of the Bc group again shows (Table 3) higher indel rates at the tip of phylogeny. Genome size variation is well known as a problem in genome content phylogeny reconstruction, but it has been noted that phylogeny, rather than phenotype or LGT, is the major quantitative determinant of gene content (Snel et al. 1999).

The more recently transferred genes have longer tree length (with P < 0.001 in a Wilcoxon rank test) (Fig. (Fig.4),4), suggesting that the recently transferred genes are evolving faster than ancient genes. The K_a/K_s ratio study suggests that, in general, more recently transferred genes have less functional constraints (Fig. (Fig.5).5). The different subfigures show the K_a/K_s ratio in genes with increasing depth in the phylogeny. Those genes that are inferred to have arisen recently via LGT in the phylogeny have a higher ratio than those that were transferred somewhat more distantly (Fig. 5, A vs. B is P ≈ 0.003954). As the length of time that the genes have been resident within the host increases, the K_a/K_s ratio continues to go down (Fig. 5, B vs. D is P ≈ 0.001618). Hence, genes that have been recently transferred into these hosts have a higher percentage of nonsynonymous substitutions. Together, the recently transferred genes not only have faster evolutionary change but also have higher K_a/K_s ratios. Similarly, a previous study reported that orphans in Escherichia coli have relatively high K_a/K_s ratios (Daubin and Ochman 2004).

This study demonstrates that more recently transferred genes are under relaxed and faster evolution compared with the genes that have had a longer residence time. There are several possible reasons for this. It is possible that the laterally transferred genes with a higher rate are more prone to being laterally transferred. This is unlikely, as genes with a slightly longer residence time should not show the observed reduced rates of evolution. It has also been suggested that genes inserted into a new host will undergo amelioration of their sequence (Lawrence and Ochman 1997). In this process, the codon and base content bias of a new gene will mutate to more closely resemble the inherent bias within the new host. It is therefore plausible to explain the higher rates of evolution in recently transferred genes compared to the completely ameliorated/native genes (Fig. (Fig.4).4). It is more difficult to see how amelioration could also cause an increase in the nonsynonymous/synonymous ratio. Amelioration is unlikely to be the main force increasing the K_a/K_s ratio in recently transferred genes since nonsynonymous sites should be affected more slowly than synonymous sites. In addition, the ratio hides the fact that the K_a value itself is much larger in many recently transferred genes (Supplemental material), again suggesting that simple amelioration is unlikely to be the cause.

The evolutionary history of the Bc group has been reconstructed using the nucleotide sequences of the gmk, glpF, and pycA genes (Priest et al. 2004) because the rRNA sequences are too similar to provide reliable evolutionary relationships. In this study, the concatenated DNA sequences of these three genes from each genome were used to reconstruct a phylogeny using Mr.Bayes (Huelsenbeck and Ronquist 2001) (200,000 generations sampled every 100 generations with a gamma distribution model and invariant class). The method to identify members of a gene family has been described in Hao and Golding (2004). In short, potential homologs were measured according to sequence similarities, and all paralogs in each genome were clustered as a single gene family and only one member was retained for further analysis. Non-annotated proteins in a genome were identified by carrying out a TBLASTN search against the DNA sequence of each genome and using all annotated proteins from other Bacillaceae genomes as query sequences. Potential taxon species genes are determined by searching against all completed bacterial genomes. (The GenBank accession numbers are given as Supplemental information at http://evol.biology.mcmaster.ca/~weilong/likelihood.) The phyletic patterns (gene presence or absence in each genome) of all genes were used for the maximum likelihood analysis.

The gene families present in the Bc group were used to conduct tree length and K_a/K_s ratio (ω) analyses using the PAML package (Yang 1997). The tree length was calculated as the sum of the branch lengths for the taxa only with the Bc group, using the maximum likelihood method from the PAML package. The tree length gives the expected number of substitutions per site along all branches in the phylogeny. Genes were categorized into four groups based on their presence/absence in different taxa (and hence on the inferred time period when the genes were transferred). The four groups are characterized by genes present only in the Bc group; genes present in Bc, Gk, Bl, and Bs; genes present in Bc, Gk, Bl, Bs, Bk, and Bh; and genes present in all 13 taxa. A single K_a/K_s ratio was assumed throughout the length of each sequence in this study. To avoid the effects of duplication during evolution (Gu et al. 2002; Zhang et al. 2003), any paralogs of gene families were excluded from the tree length and K_a/K_s ratio analyses. Protein sequences and their corresponding DNA sequences were extracted from the annotated genomes. Protein sequences were aligned using ClustalW (Thompson et al. 1994), and nucleotide sequence alignments were created from the protein alignments by replacing each amino acid with its corresponding codon.

To evaluate the likelihood of the observed phyletic patterns, a simple model of gene evolution was chosen. This model assumes that individual genes are inserted or deleted at constant rates. This model does not include a consideration of increasing or decreasing numbers of genes but, rather, a constant number of gene places that may or may not be occupied at any one time. All events are assumed to be independent. Let ν be the rate of gene insertion, and let μ be the rate of gene deletion. Let t be the length of time that separates a taxon from its ancestor. Let P indicate the gene presence, and let A indicate its absence. Then the probability of gene presence in the descendant taxon (d) can be calculated given knowledge of the state in the ancestral taxon (a). Thus, The likelihood that gene i is present at node x, with descendants y and z separated by t₁ and t₂ generations, is then calculated as For a given gene phyletic pattern i, we assume that ancestral gene presence and absence at the root of the phylogeny contribute equally to the probability of the observed pattern. Thus, the likelihood of the gene phyletic pattern i at the last common ancestral node x will be The results must also be corrected for missing data. Those genes absent in all of the taxa are unobservable. Following Felsenstein (1992), we have made a correction for the missing data in the same way as was used for missing restriction sites, and the results then are conditional on observing the gene present in at least one species. This is where Q^_−i is the likelihood of gene i being absent in all taxa. For a given phylogenetic relationship, Q^_−i will have the same value for all i.