Recent work in estimating species relationships from gene trees has included inferring networks assuming that past hybridization has occurred between species. Probabilistic models using the multispecies coalescent can be used in this framework for likelihood-based inference of both network topologies and parameters, including branch lengths and hybridization parameters. A difficulty for such methods is that it is not always clear whether, or to what extent, networks are identifiable-that is whether there could be two distinct networks that lead to the same distribution of gene trees. For cases in which incomplete lineage sorting occurs in addition to hybridization, we demonstrate a new representation of the species network likelihood that expresses the probability distribution of the gene tree topologies as a linear combination of gene tree distributions given a set of species trees. This representation makes it clear that in some cases in which two distinct networks give the same distribution of gene trees when sampling one allele per species, the two networks can be distinguished theoretically when multiple individuals are sampled per species. This result means that network identifiability is not only a function of the trees displayed by the networks but also depends on allele sampling within species. We additionally give an example in which two networks that display exactly the same trees can be distinguished from their gene trees even when there is only one lineage sampled per species. [gene tree, hybridization, identifiability, maximum likelihood, species tree, phylogeny.].

中文翻译：

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显示的树不能确定网络多物种合并下的可区分性

最近从基因树估计物种关系的工作包括推断网络，假设过去的杂交发生在物种之间。使用多物种聚结的概率模型可以在该框架中用于网络拓扑和参数（包括分支长度和杂交参数）的基于似然推断。这种方法的一个困难在于，并不总是清楚网络是否或在多大程度上是可识别的——即是否可能有两个不同的网络导致基因树的相同分布。对于除了杂交还发生不完整谱系排序的情况，我们展示了物种网络似然的新表示，它将基因树拓扑的概率分布表示为给定一组物种树的基因树分布的线性组合。这种表示清楚地表明，在某些情况下，当每个物种采样一个等位基因时，两个不同的网络给出相同的基因树分布，当每个物种采样多个个体时，这两个网络在理论上是可以区分的。这个结果意味着网络可识别性不仅是网络显示的树的函数，还取决于物种内的等位基因采样。我们还给出了一个例子，其中即使每个物种只有一个谱系采样，也可以将显示完全相同的树的两个网络与其基因树区分开来。[基因树，