## 3 Results
### Experiment I: Phylogenetic Analysis on Two Datasets
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**NO.** & **Accession Number** & **Virus Name/Strain** & **Abbreviation** \\ \hline
1 & CAB91145 & Transmissible gastroenteritis virus, genomic RNA & TGEVG \\
2 & NP.058424 & Transmissible gastroenteritis virus & TGEV \\
3 & AAK38656 & Porcine epidemic diarrhea virus strain CV777 & PEDVC \\
4 & NP.598310 & Porcine epidemic diarrhea virus & PEDV \\
5 & BAL45637 & Human coronavirus 229E & HCoV-229E \\
6 & AAP92675 & Avian infectious bronchitis virus isolate BJ & IBVBJ \\
7 & AAS00080 & Avian infectious bronchitis virus strain Ca199 & IBVC \\
8 & NP\_040831 & Avian infectious bronchitis virus & IBV \\
9 & NP\_937950 & Human coronavirus OC43 & HCoV-OC43 \\
10 & AAK83356 & Bovine coronavirus isolate BCoV-ENT & BCoVE \\
11 & AAL57308 & Bovine coronavirus isolate BCoV-LUN & BCoVL \\
12 & AAA66399 & Bovine coronavirus strain Mebus & BCoVM \\
13 & AAA40400 & Bovine coronavirus strain Quebec & BCoVCQ \\
14 & NP\_150077 & Bovine coronavirus & BCoV \\
15 & AAB86819 & Mouse hepatitis virus strain MHV-A59C12 mutant & MHVA \\
16 & YP\_209233 & Murine hepatitis virus strain HJM & MHVJHM \\
17 & AAK69334 & Mouse hepatitis virus strain Penn 97-1 & MHVP \\
18 & AAF69344 & Mouse hepatitis virus strain ML-10 & MHVM \\
19 & NP\_045300 & Mouse hepatitis virus & MHV \\
20 & AAU04646 & SARS coronavirus civet007 & civet007 \\
21 & AAU04649 & SARS coronavirus civet010 & civet010 \\
22 & AAU04664 & SARS coronavirus civet020 & civet020 \\
23 & AAV91631 & SARS coronavirus A022 & A022 \\
24 & AAV49730 & SARS coronavirus B039 & B039 \\
25 & AAP51227 & SARS coronavirus c001 & CJD01 \\
26 & AAS00003 & SARS coronavirus GZ02 & GZ02 \\
27 & AAP30030 & SARS coronavirus BJ01 & BJ01 \\
28 & AAP13567 & SARS coronavirus CUHK-W1 & CUHK-W1 \\
29 & AAP37017 & SARS coronavirus TW1 & TW1 \\
30 & AAR87523 & SARS coronavirus TW2 & TW2 \\
31 & BAC81348 & SARS coronavirus TWH genomic RNA & TWH \\
32 & BAC81362 & SARS coronavirus TWJ genomic RNA & TWJ \\
33 & AAQ01597 & SARS coronavirus Taiwan TC1 & TaiwanTC1 \\
34 & AAQ01609 & SARS coronavirus Taiwan TC2 & TaiwanTC2 \\
35 & AAP97882 & SARS coronavirus Taiwan TC3 & TaiwanTC3 \\
36 & AAP13441 & SARS coronavirus Urbani & Urbani \\
37 & AAP72986 & SARS coronavirus HSR 1 & HSR1 \\
38 & AAQ94060 & SARS coronavirus AS & AS \\
39 & AAP94737 & SARS coronavirus CUHK-AG01 & CUHK-AG01 \\
40 & AAP94748 & SARS coronavirus CUHK-AG02 & CUHK-AG02 \\
41 & AAP94759 & SARS coronavirus CUHK-AC03 & CUHK-AC03 \\
42 & AAP30713 & SARS coronavirus CUHK-Su10 & CUHK-Su10 \\
43 & AAP33697 & SARS coronavirus Frankfurt 1 & Frankfurt1 \\
44 & AAR14803 & SARS coronavirus PUMC01 & PUMC01 \\
45 & AAR14807 & SARS coronavirus PUMC02 & PUMC02 \\
46 & AAR14811 & SARS coronavirus PUMC03 & PUMC03 \\
47 & AAP41037 & SARS coronavirus TOR2 & TORE \\
48 & AAP50485 & SARS coronavirus FRA & FRA \\
49 & AAR23250 & SARS coronavirus Sin01-11 & Sino1-11 \\
50 & AHX00731 & MERS coronavirus & KFU-HKU11 \\
51 & AHX00711 & MERS coronavirus & KFU-HKU13 \\
52 & AHX00721 & MERS coronavirus & KFU-HKU19 Dam \\
53 & AIY60578 & MERS coronavirus & Abu-Dhabi\_UAE\_9 \\
54 & AIY60568 & MERS coronavirus & Abu-Dhabi\_UAE\_33 \\
55 & AIZ74417 & MERS coronavirus & Hu-France(UAE)-FRA1 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The accession number, name and abbreviation for 72 coronavirus spike proteins. The corresponding phylogenetic tree constructed by our method is shown in Figure 3. Observing Figure 3, we find that TGEVG, TGEV, PEDVC, PEDV and HCoV-229E, which belong to group alpha, are clearly clustered together, and so do the three gamma coronaviruses IBV, IBVBJ, IBVC. In the subtree of the group beta, MERS-CoVs appear to cluster together, and SARS-CoVs are situated at an independent branch, while BCoV, BCoVM, BCoVQ, BCoVE, BCoVL, HCoV-OC43, MHV, MHVA, MHVP, and MHVJHM form a separate branch. The resulting cluster agrees well with the established taxonomic groups.