Tree-average distances on certain phylogenetic networks have their weights uniquely determined.

Area of Science:

• Evolutionary Biology
• Computational Phylogenetics
• Bioinformatics

Background:

• Phylogenetic trees model species evolution, but real evolutionary histories can be more complex, involving reticulate evolution.
• Inferring evolutionary relationships from DNA data is crucial for understanding biodiversity and genetic inheritance.
• Current methods often rely on distances between extant species to infer tree structures, but these are less suited for complex networks.

Purpose of the Study:

• To propose a novel 'tree-average distance' metric applicable to phylogenetic networks, which are more general than trees.
• To develop a method for inferring the genetic change (weights) and inheritance probabilities at hybrid vertices within these networks.
• To demonstrate the unique determination of these network parameters from the proposed distance measure.

Main Methods:

• Defined a tree-average distance as the expected distance between leaf species across all possible displayed trees within a phylogenetic network.
• Assigned probabilities to inheritance events at hybrid vertices, assuming independence between these events.
• Developed a method to calculate arc weights and hybrid vertex probabilities using the tree-average distances and network structure.

Main Results:

• The tree-average distance metric was successfully defined for a class of rooted phylogenetic networks.
• It was shown that the arc weights and inheritance probabilities at hybrid vertices are uniquely determined by the network and the tree-average distances.
• The method is applicable to networks where hybrid vertices have an indegree of 2 and non-leaf vertices are tree-children.

Conclusions:

• The proposed tree-average distance provides a powerful tool for inferring the structure and parameters of complex phylogenetic networks.
• This approach offers a unique solution for estimating genetic change and inheritance probabilities, advancing phylogenetic inference beyond simple tree models.
• The findings contribute to a more accurate reconstruction of evolutionary histories, especially in cases involving hybridization or horizontal gene transfer.