Combining Orthology and Xenology Data in a Common Phylogenetic Tree - Hellmuth, Marc; Michel, Mira; Nøjgaard, Nikolai N.; Schaller, David; Stadler, Peter F. (Anais do Simpósio Brasileiro de Bioinformática (BSB); 2021: Anais do XIV Simpósio Brasileiro de Bioinformática, 2021)
In mathematical phylogenetics, types of events in a gene tree T are formalized by vertex labels t(v) and set-valued edge labels λ(e). The orthology and paralogy relations between genes are a special case of a map δ on the pairs of leaves of T defined by δ(x,y)=q if the last common ancestor lca(x,y) of x and y is labeled by an event type q, e.g., speciation or duplication. Similarly, a map ε with m∈ε(x,y) if m∈λ(e) for at least one edge e along the path from lca(x,y) to y generalizes xenology, i.e., horizontal gene transfer. We show that a pair of maps (δ,ε) derives from a tree (T,t,λ) in this manner if and only if there exists a common refinement of the (unique) least-resolved vertex labeled tree (T δ ,t δ ) that explains δ and the (unique) least-resolved edge labeled tree (T ε ,λ ε ) that explains ε (provided both trees exist). This result remains true if certain combinations of labels at incident vertices and edges are forbidden.