The species studied in any evolutionary investigation generally constitute a small proportion of all the species currently existing or that have gone extinct. It is therefore likely that introgression, which is widespread across the tree of life, involves “ghosts,” i.e., unsampled, unknown, or extinct lineages. However, the impact of ghost introgression on estimations of species trees has rarely been studied and is poorly understood. Here, we use mathematical analysis and simulations to examine the robustness of species tree methods based on the multispecies coalescent model to introgression from a ghost or extant lineage. We found that many results originally obtained for introgression between extant species can easily be extended to ghost introgression, such as the strongly interactive effects of incomplete lineage sorting (ILS) and introgression on the occurrence of anomalous gene trees (AGTs). The relative performance of the summary species tree method (ASTRAL) and the full-likelihood method (*BEAST) varies under different introgression scenarios, with the former being more robust to gene flow between non-sister species whereas the latter performing better under certain conditions of ghost introgression. When an outgroup ghost (defined as a lineage that diverged before the most basal species under investigation) acts as the donor of the introgressed genes, the time of root divergence among the investigated species generally was overestimated, whereas ingroup introgression, as commonly perceived, can only lead to underestimation. In many cases of ingroup introgression that may or may not involve ghost lineages, the stronger the ILS, the higher the accuracy achieved in estimating the time of root divergence, although the topology of the species tree is more prone to be biased by the effect of introgression.

中文翻译：

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幽灵渗入对基于聚结的物种树推断和分歧时间估计的影响

在任何进化研究中研究的物种通常只占目前存在或已经灭绝的所有物种的一小部分。因此，在整个生命之树中广泛存在的基因渗入很可能涉及“幽灵”，即未采样的、未知的或已灭绝的谱系。然而，幽灵基因渗入对物种树估计的影响很少被研究并且知之甚少。在这里，我们使用数学分析和模拟来检查基于多物种聚结模型的物种树方法对幽灵或现存谱系的渐渗的稳健性。我们发现许多最初获得的关于现存物种之间渐渗的结果可以很容易地扩展到幽灵渐渗，例如不完全谱系分类 (ILS) 和基因渗入对异常基因树 (AGT) 发生的强烈交互作用。摘要物种树法 (ASTRAL) 和全似然法 (*BEAST) 的相对性能在不同的基因渗入情况下有所不同，前者对非姐妹物种之间的基因流动更稳健，而后者在某些条件下表现更好鬼渗入。当一个外群幽灵（定义为在被调查的最基础物种之前分化的谱系）充当渗入基因的供体时，被调查物种之间根系分化的时间通常被高估，而通常认为的内渗可以只会导致低估。