Reconstructing Gene Trees From Fitch's Xenology Relation

TL;DR

This paper characterizes xenology relations among genes as a non-symmetric, heritable graph property, providing a linear-time recognition algorithm and a method to reconstruct a unique least-resolved phylogenetic tree.

Contribution

It introduces a characterization of xenology relations via forbidden subgraphs and offers a linear-time algorithm for their recognition and tree reconstruction.

Findings

Xenology relations are characterized by forbidden induced subgraphs.

Each xenology relation corresponds to a unique least-resolved phylogenetic tree.

Recognition and reconstruction algorithms run in linear time.

Abstract

Two genes are xenologs in the sense of Fitch if they are separated by at least one horizontal gene transfer event. Horizonal gene transfer is asymmetric in the sense that the transferred copy is distinguished from the one that remains within the ancestral lineage. Hence xenology is more precisely thought of as a non-symmetric relation: $y$ is xenologous to $x$ if $y$ has been horizontally transferred at least once since it diverged from the least common ancestor of $x$ and $y$. We show that xenology relations are characterized by a small set of forbidden induced subgraphs on three vertices. Furthermore, each xenology relation can be derived from a unique least-resolved edge-labeled phylogenetic tree. We provide a linear-time algorithm for the recognition of xenology relations and for the construction of its least-resolved edge-labeled phylogenetic tree. The fact that being a xenology relation is a heritable graph property, finally has far-reaching consequences on approximation problems associated with xenology relations.