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. 2007 Oct 5:8:374.
doi: 10.1186/1471-2105-8-374.

Statistical power of phylo-HMM for evolutionarily conserved element detection

Xiaodan Fan  1 , Jun Zhu, Eric E Schadt, Jun S Liu
Affiliations

Statistical power of phylo-HMM for evolutionarily conserved element detection

Xiaodan Fan et al. BMC Bioinformatics. .

Abstract

Background: An important goal of comparative genomics is the identification of functional elements through conservation analysis. Phylo-HMM was recently introduced to detect conserved elements based on multiple genome alignments, but the method has not been rigorously evaluated.

Results: We report here a simulation study to investigate the power of phylo-HMM. We show that the power of the phylo-HMM approach depends on many factors, the most important being the number of species-specific genomes used and evolutionary distances between pairs of species. This finding is consistent with results reported by other groups for simpler comparative genomics models. In addition, the conservation ratio of conserved elements and the expected length of the conserved elements are also major factors. In contrast, the influence of the topology and the nucleotide substitution model are relatively minor factors.

Conclusion: Our results provide for general guidelines on how to select the number of genomes and their evolutionary distance in comparative genomics studies, as well as the level of power we can expect under different parameter settings.

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Figures

Figure 1
Figure 1
Two-state phylo-HMM. (A) State-transition diagram: The system consists of a state for conserved sites (c) and a state for nonconserved sites (n). The two states are associated with different phylogenetic models (ψc and ψn). The state-transition probabilities are defined by two parameters (μ and ν) as illustrated. (B) An illustrative alignment generated by this model: A state sequence (Z) is generated according to μ and ν. For each site in the state sequence, a nucleotide is generated for the root node in the phylogenetic tree and then for subsequent child node according to the phylogenetic model (ψc or ψn). The observed alignment (X) is composed of all nucleotides in the leaf nodes. The segment of adjacent conserved sites (in the gray box) is called a conserved element.
Figure 2
Figure 2
Topology of the baseline phylogenetic tree. For the un-rooted version of this tree, the branch between the mouse-rat and the human-dog pairs is called the "middle branch".
Figure 3
Figure 3
Power comparison at the baseline. The red solid line is the ROC curve for the phylo-HMM method. The blue dashed line is the ROC curve for the PID method (window size = 51 bp). The points indicate the median sensitivity and specificity values. The green crosses show their 1st-to-3rd quartile range when the threshold is set as the labeled value. The black crosses show the corresponding 95% bootstrap confidence interval of the median sensitivity and specificity.
Figure 4
Figure 4
The relationship between the median sensitivity and branch length at different locations in the tree. The specificity is fixing at 0.9. The different lines represent the different branches as illustrated in the legend. The green dot indicates the length of the corresponding branch at the baseline. The green whiskers at r = 0, 0.9 and 3 indicate the 95% bootstrap confidence interval for the median sensitivity.
Figure 5
Figure 5
Power comparison for different topologies. (A) Topologies considered. Topologies in the same row have the same total branch length and same number of comparative genomes. Each column corresponds to a class of topologies. One unit branch length is 0.196199 substitutions per site (mouse-rat like). The number of comparative genomes is equal to the number of units. For topologies with balanced branch lengths, all branches have the same length. For topologies with unbalanced branch lengths, all branches except the long branch have length equal to 0.02 substitutions per site. The length of the long branch is set to make the total branch length equal to 8 units. (B) Corresponding ROC curves. As illustrated in the legend, the different groups of curves represent different topology classes. Different point groups highlighted along the curves represent the different rows in Figure 5(A). The locations of these points correspond to a posterior probability threshold equal to 0.5. The crosses show the 1st-to-3rd quartile range of the sensitivity and specificity.
Figure 6
Figure 6
Influence of the number of genomes for the symmetric star topology. This graph illustrates the relationship between one over the number of genomes and the individual branch lengths. The specificity is fixed at 0.95 in all cases. Each curve corresponds to a given sensitivity (Sn) level as illustrated in the legend.
Figure 7
Figure 7
Influence of substitution model type. This graph compares the power of phylo-HMM for (A) different substitution model types (JC, F81 with baseline π, HKY with kappa = 4 and baseline π, REV with baseline π and rate matrix), and (B) simulations carried out using the REV model and then estimations carried out using the JC and REV models. The curves again represent the ROC curves as defined in the legend. The crosses highlight points corresponding to the 0.5 posterior probability threshold. The small solid line crosses in (B) show the 95% bootstrap confidence interval of the median sensitivity and specificity. Other crosses show the 1st-to-3rd quartile range.
Figure 8
Figure 8
Power comparison of phylo-HMM for different expected coverage of conserved element (P) and expected element length (L). The black dotted lines are the ROC curves for the P&L setting as annotated. For example "P0.05L10" means P = 0.05 and L = 10. The points are their power at posterior probability threshold equal to 0.5. The point corresponding to the baseline (P0.25L50) is indicated as a green dot. The blue solid lines connect the points with the same P, while the red dashed line connects the points with the same L. Some of the points are highlighted by crosses. The green dotted line crosses show the 1st-to-3rd quartile range. The black solid line crosses show the 95% bootstrap confidence interval of the median sensitivity and specificity.
Figure 9
Figure 9
Power comparison of phylo-HMM for different conservation ratio (ρ). (A) Comparing the whole ROC curves. The ROC curves shown are for different ρ as illustrated in the legend. The locations of the points correspond to a posterior probability threshold equal to 0.5. Some of the points are highlighted by crosses. The red dotted line crosses show the 1st-to-3rd quartile range. The black solid line crosses show the 95% bootstrap confidence interval of the median sensitivity and specificity. (B) The relationship between sensitivity and the conservation ratio at a fixed specificity equal to 0.9. The dots are where power was evaluated by simulation. The red whiskers at ρ = 0.3, 0.5, and ρ = 0.7 indicate the 95% bootstrap confidence interval for the median sensitivity. The red triangle indicates the power of the baseline, where ρ = 0.32.
Figure 10
Figure 10
The relationship between the column score and branch length. (A) Relationships for branches at different locations in the baseline phylogenetic tree. The different lines represent the different branches as illustrated in the legend. (B) Relationships for branches in the symmetric star-topology tree. The different lines correspond to the different numbers of genomes (n) represented by the tree.
Figure 11
Figure 11
The influence of alignment quality to the power of phylo-HMM. Simulations were done by varying the length of the middle branch in the baseline phylogenetic tree. The black solid line shows the relationship between the branch length and the column score. The red and blue dashed lines show the relationships between the branch length and the median sensitivity for the true and the recovered alignments, respectively, with the specificity fixed at 0.9.
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