BACKGROUND In the absence of horizontal gene transfer it is possible to reconstruct the history of gene families from empirically determined orthology relations, which are equivalent to event-labeled gene trees. Knowledge of the event labels considerably simplifies the problem of reconciling a gene tree T with a species trees S, relative to the reconciliation problem without prior knowledge of the event types. It is well-known that optimal reconciliations in the unlabeled case may violate time-consistency and thus are not biologically feasible. Here we investigate the mathematical structure of the event labeled reconciliation problem with horizontal transfer. RESULTS We investigate the issue of time-consistency for the event-labeled version of the reconciliation problem, provide a convenient axiomatic framework, and derive a complete characterization of time-consistent reconciliations. This characterization depends on certain weak conditions on the event-labeled gene trees that reflect conditions under which evolutionary events are observable at least in principle. We give an [Formula: see text]-time algorithm to decide whether a time-consistent reconciliation map exists. It does not require the construction of explicit timing maps, but relies entirely on the comparably easy task of checking whether a small auxiliary graph is acyclic. The algorithms are implemented in C++ using the boost graph library and are freely available at https://github.com/Nojgaard/tc-recon. SIGNIFICANCE The combinatorial characterization of time consistency and thus biologically feasible reconciliation is an important step towards the inference of gene family histories with horizontal transfer from orthology data, i.e., without presupposed gene and species trees. The fast algorithm to decide time consistency is useful in a broader context because it constitutes an attractive component for all tools that address tree reconciliation problems.

中文翻译：

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时间一致的和解地图和禁止的时间旅行。

背景在没有水平基因转移的情况下，可以根据经验确定的直系关系重建基因家族的历史，这相当于事件标记的基因树。相对于没有事件类型先验知识的协调问题，事件标签的知识大大简化了协调基因树 T 与物种树 S 的问题。众所周知，未标记情况下的最优协调可能会违反时间一致性，因此在生物学上是不可行的。在这里，我们研究了带有水平转移的事件标记和解问题的数学结构。结果我们调查了协调问题的事件标记版本的时间一致性问题，提供了一个方便的公理框架，并得出时间一致和解的完整特征。这种表征取决于事件标记基因树上的某些弱条件，这些条件反映了至少在原则上可以观察到进化事件的条件。我们给出一个[公式：见正文]-时间算法来决定是否存在时间一致的协调图。它不需要构建显式时序图，而是完全依赖于检查小辅助图是否是非循环的相对简单的任务。这些算法使用 boost 图形库在 C++ 中实现，可在 https://github.com/Nojgaard/tc-recon 免费获得。意义 时间一致性的组合表征和因此生物学上可行的协调是朝着从正交数据水平转移推断基因家族历史的重要一步，即，没有预先假定的基因和物种树。决定时间一致性的快速算法在更广泛的背景下很有用，因为它构成了所有解决树协调问题的工具的有吸引力的组件。