Combining Orthology and Xenology Data in a Common Phylogenetic Tree

TL;DR

This paper establishes a theoretical framework for reconstructing a common phylogenetic tree from paired orthology and xenology data, showing how such data can be integrated via least-resolved trees.

Contribution

It introduces a characterization of when pairs of maps from leaf pairs can be derived from a single phylogenetic tree, linking orthology and xenology data in a unified model.

Findings

A pair of maps can be explained by a common tree if and only if certain least-resolved trees exist.

The framework accommodates forbidden label combinations at vertices and edges.

Provides conditions for the existence of a common refinement explaining both data types.

Abstract

A rooted tree $T$ with vertex labels $t(v)$ and set-valued edge labels $\lambda(e)$ defines maps $\delta$ and $\varepsilon$ on the pairs of leaves of $T$ by setting $\delta(x,y)=q$ if the last common ancestor $\text{lca}(x,y)$ of $x$ and $y$ is labeled $q$, and $m\in \varepsilon(x,y)$ if $m\in\lambda(e)$ for at least one edge $e$ along the path from $\text{lca}(x,y)$ to $y$. We show that a pair of maps $(\delta,\varepsilon)$ derives from a tree $(T,t,\lambda)$ if and only if there exists a common refinement of the (unique) least-resolved vertex labeled tree $(T_{\delta},t_{\delta})$ that explains $\delta$ and the (unique) least resolved edge labeled tree $(T_{\varepsilon},\lambda_{\varepsilon})$ that explains $\varepsilon$ (provided both trees exist). This result remains true if certain combinations of labels at incident vertices and edges are forbidden.