Path lengths in tree-child time consistent hybridization networks

TL;DR

This paper extends path length-based metrics from phylogenetic trees to tree-child time consistent hybridization networks, enabling their comparison and assessment in evolutionary studies.

Contribution

It introduces vector-based metrics for TCTC hybridization networks, generalizing known tree metrics and proving their effectiveness for network isomorphism detection.

Findings

Vectors of splitted path lengths uniquely identify TCTC hybridization networks.

Metrics based on these vectors form a valid distance measure for TCTC networks.

Simpler vectors suffice for fully resolved hybridization networks.

Abstract

Hybridization networks are representations of evolutionary histories that allow for the inclusion of reticulate events like recombinations, hybridizations, or lateral gene transfers. The recent growth in the number of hybridization network reconstruction algorithms has led to an increasing interest in the definition of metrics for their comparison that can be used to assess the accuracy or robustness of these methods. In this paper we establish some basic results that make it possible the generalization to tree-child time consistent (TCTC) hybridization networks of some of the oldest known metrics for phylogenetic trees: those based on the comparison of the vectors of path lengths between leaves. More specifically, we associate to each hybridization network a suitably defined vector of `splitted' path lengths between its leaves, and we prove that if two TCTC hybridization networks have the same such vectors, then they must be isomorphic. Thus, comparing these vectors by means of a metric for real-valued vectors defines a metric for TCTC hybridization networks. We also consider the case of fully resolved hybridization networks, where we prove that simpler, `non-splitted' vectors can be used.