A labeled gene tree topology that is more probable than the labeled gene tree topology matching a species tree is called "anomalous." Species trees that can generate such anomalous gene trees are said to be in the "anomaly zone." Here, probabilities of "unranked" and "ranked" gene tree topologies under the multispecies coalescent are considered. A ranked tree depicts not only the topological relationship among gene lineages, as an unranked tree does, but also the sequence in which the lineages coalesce. In this article, we study how the parameters of a species tree simulated under a constant-rate birth-death process can affect the probability that the species tree lies in the anomaly zone. We find that with more than five taxa, it is possible for species trees to have both anomalous unranked and ranked gene trees. The probability of being in either type of anomaly zone increases with more taxa. The probability of anomalous gene trees also increases with higher speciation rates. We observe that the probabilities of unranked anomaly zones are higher and grow much faster than those of ranked anomaly zones as the speciation rate increases. Our simulation shows that the most probable ranked gene tree is likely to have the same unranked topology as the species tree. We design the software PRANC, which computes probabilities of ranked gene tree topologies given a species tree under the coalescent model.

中文翻译：

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出生-死亡模型下未排序和排序的异常区域的概率。

与匹配物种树的标记基因树拓扑相比，标记基因树拓扑更有可能被称为“异常”。可以生成此类异常基因树的物种树被称为“异常区”。在这里，考虑了多物种合并下的“未排序”和“排序”基因树拓扑的概率。排序的树不仅像未排序的树那样描述基因谱系之间的拓扑关系，而且还描​​述谱系合并的顺序。在本文中，我们研究在恒定速率的出生-死亡过程下模拟的树的参数如何影响树在异常区域中的概率。我们发现有五个以上的分类单元 物种树可能同时具有未排序的异常树和已排序的基因树。随着更多的分类单元，处于两种类型的异常区域的可能性都会增加。基因树异常的可能性也随着更高的物种形成率而增加。我们观察到，随着物种形成率的增加，未排序异常区域的概率比已排序异常区域的概率更高，并且增长得更快。我们的模拟表明，最有可能排名的基因树可能具有与物种树相同的未排名拓扑。我们设计了软件PRANC，该软件可在合并模型下计算给定物种树的排名基因树拓扑的概率。我们观察到，随着物种形成率的增加，未排序异常区域的概率比已排序异常区域的概率更高，并且增长得更快。我们的模拟表明，最有可能排名的基因树可能具有与物种树相同的未排名拓扑。我们设计了软件PRANC，该软件可在合并模型下计算给定物种树的排名基因树拓扑的概率。我们观察到，随着物种形成率的增加，未排序异常区域的概率比已排序异常区域的概率更高，并且增长得更快。我们的模拟表明，最有可能排名的基因树可能具有与物种树相同的未排名拓扑。我们设计了软件PRANC，该软件可在合并模型下计算给定物种树的排名基因树拓扑的概率。