在共同的系统发育树中结合正骨学和异种学数据
Combining Orthology and Xenology Data in a Common Phylogenetic Tree
摘要：
具有顶点标签$t(v)$和集值边标签$λ(e)$的根树$T$通过在$x$和$y$的最后共同祖先$\text{lca}(x,y)$被标记为$q$的情况下设置$δ(x,y)=q$以及在$m\inλ(e)$的情况下设置$m\in \varepsilon(x,y)$来定义$T$的成对叶上的映射$δ$和$\varepsilon$，其中$e$沿着从$\text{lca}(x,y)$到$y$的路径用于至少一个边$e$。我们表明，一对地图$(δ,\varepsilon)$来自树$(T,t,λ)$当且仅当存在一个共同的细化（唯一）最低分辨率顶点标记树$(T_δ,t_δ)$解释$δ$和（唯一）最低分辨率边标记树$(T_{\varepsilon},λ_{\varepsilon})$解释$\varepsilon$（假设两棵树都存在）。如果禁止关联顶点和边处的标签的某些组合，则该结果仍然成立。
英文摘要：
A rooted tree $T$ with vertex labels $t(v)$ and set-valued edge labels $λ(e)$ defines maps $δ$ and $\varepsilon$ on the pairs of leaves of $T$ by setting $δ(x,y)=q$ if the last common ancestor $\text{lca}(x,y)$ of $x$ and $y$ is labeled $q$, and $m\in \varepsilon(x,y)$ if $m\inλ(e)$ for at least one edge $e$ along the path from $\text{lca}(x,y)$ to $y$. We show that a pair of maps $(δ,\varepsilon)$ derives from a tree $(T,t,λ)$ 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 $(T_{\varepsilon},λ_{\varepsilon})$ that explains $\varepsilon$ (provided both trees exist). This result remains true if certain combinations of labels at incident vertices and edges are forbidden.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
