{"paper":{"title":"Combining Orthology and Xenology Data in a Common Phylogenetic Tree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","q-bio.PE"],"primary_cat":"math.CO","authors_text":"David Schaller, Marc Hellmuth, Mira Michel, Nikolai N. N{\\o}jgaard, Peter F. Stadler","submitted_at":"2021-07-05T09:33:54Z","abstract_excerpt":"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 expla"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.01893","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2107.01893/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}