BACKGROUND The history of gene families-which are equivalent to event-labeled gene trees-can be reconstructed from empirically estimated evolutionary event-relations containing pairs of orthologous, paralogous or xenologous genes. The question then arises as whether inferred event-labeled gene trees are biologically feasible, that is, if there is a possible true history that would explain a given gene tree. In practice, this problem is boiled down to finding a reconciliation map-also known as DTL-scenario-between the event-labeled gene trees and a (possibly unknown) species tree. RESULTS In this contribution, we first characterize whether there is a valid reconciliation map for binary event-labeled gene trees T that contain speciation, duplication and horizontal gene transfer events and some unknown species tree S in terms of "informative" triples that are displayed in T and provide information of the topology of S. These informative triples are used to infer the unknown species tree S for T. We obtain a similar result for non-binary gene trees. To this end, however, the reconciliation map needs to be further restricted. We provide a polynomial-time algorithm to decide whether there is a species tree for a given event-labeled gene tree, and in the positive case, to construct the species tree and the respective (restricted) reconciliation map. However, informative triples as well as DTL-scenarios have their limitations when they are used to explain the biological feasibility of gene trees. While reconciliation maps imply biological feasibility, we show that the converse is not true in general. Moreover, we show that informative triples neither provide enough information to characterize "relaxed" DTL-scenarios nor non-restricted reconciliation maps for non-binary biologically feasible gene trees.

中文翻译：

---

生物学上可行的基因树、协调图和信息三元组。


背景技术基因家族的历史——相当于事件标记的基因树——可以根据经验估计的包含直系同源、旁系同源或异种基因对的进化事件关系来重建。接下来的问题是，推断的事件标记基因树在生物学上是否可行，即是否存在可能的真实历史来解释给定的基因树。在实践中，这个问题归结为在事件标记的基因树和（可能未知的）物种树之间找到协调图（也称为 DTL 场景）。结果在这篇文章中，我们首先描述了包含物种形成、复制和水平基因转移事件的二元事件标记基因树 T 和一些未知物种树 S 是否存在有效的调节图，这些基因树显示在“信息性”三元组方面。 T 并提供 S 的拓扑信息。这些信息三元组用于推断 T 的未知物种树 S。我们对非二元基因树获得了类似的结果。然而，为此，调节图需要进一步限制。我们提供了一种多项式时间算法来确定给定的事件标记基因树是否存在物种树，并在肯定的情况下构建物种树和相应的（受限的）协调图。然而，信息三元组和 DTL 场景在用于解释基因树的生物学可行性时有其局限性。虽然协调图意味着生物学可行性，但我们表明反之通常并不成立。 此外，我们表明，信息三元组既不能提供足够的信息来表征“宽松的”DTL 场景，也不能提供非二元生物学上可行的基因树的非限制性协调图。