The dataset used in this study is:

• Covid-19_trees.txt

This file contains multiple phylogenetic trees in Newick format, representing different possible evolutionary relationships between coronavirus strains.

Example (excerpt):

(Guangxi_Pangolin_P2V,...,Hu_Wuhan_2020,...)

👉 These trees include:

• Human COVID-19 sequences (Wuhan, USA, Italy, Australia)
• Bat coronaviruses (RaTG13, Bat-CoV)
• Pangolin coronaviruses
• Other related viruses (SARS, MERS)

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The application was executed using:

• Cluster validity index: CH (Calinski-Harabasz)
• α (penalty parameter): 0.2
• K range: [3, 8]

CH;12;...;4;4;1.000;...;part(1 <> 1 <> 1 <> 3 <> ... <> 4)

• Optimal number of clusters: K = 4
• Perfect clustering score: 1.000
• Partition distribution:

part(1 <> 1 <> 1 <> 3 <> 1 <> 1 <> 1 <> 1 <> 1 <> 1 <> 2 <> 4)

👉 This means:

• Most trees belong to Cluster 1
• Some trees belong to clusters 2, 3, and 4

This cluster contains the majority of trees:

• T1, T2, T3, T5, T6, T7, T8 ...

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These trees share a common evolutionary structure:

• Human COVID-19 strains are grouped together
• Close relationship with RaTG13 (bat virus)
• Pangolin viruses appear as intermediate

👉 This cluster represents:

The dominant evolutionary hypothesis of SARS-CoV-2

Clusters 2, 3, and 4 contain fewer trees.

👉 Interpretation:

• Alternative evolutionary scenarios
• Possible variations due to:
  • different tree inference methods
  • uncertainty in data
  • genetic variability

This study highlights an important concept:

Because:

• Different datasets
• Different inference algorithms
• Biological uncertainty

KMPTC helps to:

• Group similar trees using RF distance
• Identify dominant evolutionary patterns
• Reduce complexity from many trees to a few clusters

From this clustering:

• A main evolutionary pattern emerges (Cluster 1)
• Several alternative hypotheses exist (Clusters 2–4)

• COVID-19 strains are closely related worldwide
• Strong evolutionary link with bat coronavirus (RaTG13)
• Pangolin viruses may play a role in intermediate evolution

This case study demonstrates that:

• K-means + RF distance effectively groups phylogenetic trees
• Clustering reveals dominant evolutionary scenarios
• Supertrees can summarize complex biological relationships

👉 The method transforms:

Many uncertain trees → Few meaningful evolutionary patterns

• RF distance measures structural differences between trees
• K-means groups similar evolutionary hypotheses
• CH index selects the optimal number of clusters
• Each cluster represents a biological interpretation
• Supertrees summarize evolutionary patterns