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arXiv · 2107.01893

Combining Orthology and Xenology Data in a Common Phylogenetic Tree

Marc Hellmuth·Mira Michel·Nikolai N. Nøjgaard·David Schaller·Peter F. Stadler
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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.

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BibTeXRIS

Marc Hellmuth, Mira Michel, Nikolai N. Nøjgaard, David Schaller, Peter F. Stadler. 2021-07-05. Combining Orthology and Xenology Data in a Common Phylogenetic Tree. https://arxiv.org/abs/2107.01893

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