# Three-Way Alignment Improves Multiple Sequence Alignment of Highly Diverged Sequences
## 3 Results
### Three-Way Alignment Leads to More Accurate Phylogenetic Results than Other Approaches  
How will the difference in the guide tree affect the final phylogenetic reconstruction? We obtained MSA from each of the three types of guide trees as follows: (1) the true tree used for sequence simulation, (2) the guide tree reconstructed by the L-INS-i approach, and (3) the guide tree from the three-way alignment (3-WAY in Table 3). These MSAs are then used to reconstruct phylogenies by PhyML. We expect the MSAs obtained with the true tree as the guide tree to recover true trees but are interested in whether the three-way alignment approach will outperform the L-INS-i approach. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Symmetric Tree**} & \multicolumn{3}{c}{**Asymmetric Tree**} \\ \hline
**Guide Tree** & **Ntrue (1)** & **RFd (2)** & **SERFd (3)** & **Ntrue (1)** & **RFd (2)** & **SERFd (3)** \\ \hline L-INS-i & 27 & 0.92 & 0.1424 & 0 & 5.12 & 0.1993 \\ \hline
3-WAY & 31 & 0.76 & 0.1387 & 0 & 4.84 & 0.2067 \\ \hline \hline \end{tabular} \({}^{(1)}\) N\({}_{\text{true}}\): the number of correctly reconstructed trees (RFd = 0) using a method. \({}^{(2)}\) RFd: mean RFd from 50 simulated sets of sequences. \({}^{(3)}\) SE\({}_{\text{RFd}}\): standard error of RFd.  
\end{table} 
Table 1: Result of comparing guide trees generated using 3-way alignment and L-INS-i methods based on simulated amino acid sequences on 8-taxa symmetric and asymmetric trees. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**H-S Tree**} & \multicolumn{3}{c}{**S Tree**} & \multicolumn{3}{c}{**H-AS Tree**} & \multicolumn{3}{c}{**AS Tree**} \\ \hline
**Guide Tree** & **Ntrue** & **RFd** & **SERFd** & **Ntrue** & **RFd** & **SERFd** & **Ntrue** & **RFd** & **SERFd** & **Ntrue** & **RFd** & **SERFd** \\ \hline FFT-NS-1 & 35 & 1.08 & 0.2693 & 0 & 9.24 & 0.5107 & 15 & 2.52 & 0.3514 & 0 & 15.32 & 0.5817 \\ \hline FFT-NS-2 & 34 & 1.28 & 0.2956 & 0 & 7.24 & 0.4495 & 29 & 1.16 & 0.2497 & 0 & 13 & 0.4891 \\ \hline L-INS-i & 50 & 0 & 0 & 39 & 0.6 & 0.1429 & 41 & 0.36 & 0.1098 & 0 & 6.48 & 0.2325 \\ \hline
3-WAY & 50 & 0 & 0 & 40 & 0.4 & 0.1143 & 39 & 0.52 & 0.1491 & 3 & 5.8 & 0.3886 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Quality of guide trees generated using three MAFFT options (FFT-NS-1, FFT-NS-2, L-INS-i) and the 3-way alignment (3-WAY), based on simulated amino acid sequences the 16-taxa trees, including half-symmetric (H-S tree), symmetric (S tree), half-asymmetric (H-AS tree), and asymmetric (AS tree) trees. Other column labels are the same as in Table 1.  
Using the true tree as the guide tree apparently increases the chance of the true tree being recovered through the aligned sequences, which is true for both the 8-taxa symmetric and asymmetric trees (Table 3). With the symmetric tree, the three-way alignment approach outperformed the L-NS-i approach, recovering more true trees and having a smaller mean RFd (Table 3). However, the difference is not statistically significant given the sample size of 50 for each group (two-tailed paired-sample \(t\)-test, t = 1.4289, DF = 49, \(p\) = 0.1594). With the asymmetric tree, none of the 50 MSAs from the L-INS-i approach recovered a true tree, and neither did the three-way alignment approach (Table 3). However, the RFd is smaller for the three-way alignment approach (mean RFd = 5) than that of the L-NS-i approach (RFd = 6). The difference is statistically significant based on a paired-sample \(t\)-test (t = 3.6293, DF = 49, \(p\) = 0.0007). This difference between the L-INS-i and the three-way alignment approach is also consistent with the results in Table 1.  
We also performed the same comparison of phylogenetic results from the 16-taxa trees (Table 4). We compared the accuracy of the reconstructed phylogenetic trees from the FFT-NS-1, FFT-NS-2, L-INS-i, and three-way alignment methods.