# Three-Way Alignment Improves Multiple Sequence Alignment of Highly Diverged Sequences
## 3 Results
### Sum-of-Pair Score May Not Be a Good Criterion for Choosing the Best MSA  
There are two criteria that can be used to evaluate the quality of an MSA. The first is phylogenetic accuracy, i.e., the MSA that results in the most accurate phylogenetic reconstruction is the best MSA. This criterion is conceptually fine but not computationally practical. Also, one can generally evaluate phylogenetic accuracy only for simulated sequences with a known true tree. The second criterion is the sum-of-pair score (SPS) or its variations, such as weighted SPS [39; 40; 41]. This weighted SPS is used in the default option in MUSCLE and the G-INS-i and L-INS-i options in MAFFT. The criterion is computationally practical and expected to be generally consistent with the first criterion. Our results in the previous section show that when an MSA is generated with the true tree as a guide tree, this MSA tends to result in the most accurate phylogenetic reconstruction. It is, therefore, interesting to know if an MSA generated with the true tree as a guide tree also leads to the highest SPS. We compared SPS from two types of MSAs, one generated using the true tree as the guide tree (the \"trueTree\" approach) and the other generated using the accurate L-INS-i option (the \"L-INS-i\" approach, which creates the guide tree based on local pairwise alignment) in MAFFT. The input sequences are simulated with symmetric and asymmetric trees as before, with an average sequence length of 500 amino acids. Each simulated data set generated two MSAs, one from the trueTree approach and the other from the L-INS-i approach. The two MSAs were also used for phylogenetic reconstruction using PhyML. When the true tree was used as a guide tree, the final PhyML tree was closer to the true tree (smaller RFd) than that of the L-INS-i approach (Figure 5A,C). This difference is highly significant based on a paired-sample \(t\)-test (\(p<0.0001\) for data in Figure 5A,C). Thus, when  
Figure 4: Relationship between RFd of guide trees and RFd of phylogenetic trees generated by PhyML, based on 16-taxa trees. (**A**) FFT-NS-1 approach in which the guide tree was generated from 6-tuple similarities. (**B**) FFT-NS-2 approach in which the guide tree is recomputed from the first round of multiple sequence alignment. (**C**) L-INS-i approach in which the guide tree is from local pairwise alignment. (**D**) Three-way alignment approach in which the guide tree was described in the Section 2. A bubble plot was used because many points overlapped with each other. phylogenetic accuracy is used as a criterion, the MSA resulting from using the true tree as a guide tree is better than MSA from the L-INS-i approach. Surprisingly, SPS is higher for the MSA from the L-INS-i than the MSA from using the true tree as the guide tree (Figure 5B,C). This is consistent for both the asymmetric tree and the symmetric tree. The difference is highly significant based on a paired-sample \(t\)-test (\(p<0.0001\)). This creates a conflict in choosing the best MSA. With the criterion of phylogenetic accuracy as a criterion, the MSA from the trueTree approach is better; with the SPS as the criterion, the MSA from the L-INS-i approach is better. To further confirm the results in Figure 5, we simulated longer sequences with an average length of 1500 amino acids according to those symmetric and asymmetric trees. The same computation was repeated. For asymmetric trees (Figure 6A), the trueTree approach (MSA obtained with the true tree as a guide tree) generated PhyML trees more similar than those generated from the L-INS-i approach. This difference in RFd between the trueTree and the L-INS-i approaches is highly significant (paired-sample \(t\)-test, \(p<0.0001\)). The longer sequence length allowed both the trueTree and the L-INS-i approaches to recover all symmetric true trees (Figure 6C). Thus, the criterion of phylogenetic accuracy still favors the trueTree approach over the L-INS-i approach. The relevant scatter plots for dataset used in Figures 5 and 6 are provided in Supplementary Materials.