When two trees go to war.

Area of Science:

• Evolutionary biology
• Computational phylogenetics
• Network theory

Background:

• Phylogenetic networks model non-treelike evolutionary histories by integrating diverse data types.
• Commonly used models include trees, clusters, triplets, and characters.
• Minimizing reticulation events (non-treelike evolutionary events) is a key goal in network construction.

Purpose of the Study:

• To review and investigate the relationships between four distinct models for constructing rooted phylogenetic networks.
• To determine if the choice of model affects the minimum number of reticulations required for network construction.
• To unify computational complexity questions in phylogenetic network inference.

Main Methods:

• Comparative analysis of four rooted phylogenetic network models: trees, clusters, triplets, and characters.
• Investigation of network construction based on minimizing reticulation events (parsimony principle).
• Examination of network construction based on minimizing network level.

Main Results:

• When input data consists of two binary trees, the minimum number of reticulations is model-independent.
• The number of reticulations required is equal across models for trees, triplets, clusters, and characters.
• This unification holds true when minimizing network level instead of reticulations.
• Model divergence is observed when data from three binary trees is used.

Conclusions:

• The study unifies several models for rooted phylogenetic networks under specific conditions, particularly with binary tree inputs.
• This unification simplifies understanding and computation for phylogenetic network construction.
• The findings resolve long-standing computational complexity questions in the field.