Inference of the evolutionary histories of species, commonly represented by a species tree, is complicated by the divergent evolutionary history of different parts of the genome. Different loci on the genome can have different histories from the underlying species tree (and each other) due to processes such as incomplete lineage sorting (ILS), gene duplication and loss, and horizontal gene transfer. The multispecies coalescent is a commonly used model for performing inference on species and gene trees in the presence of ILS. This paper introduces Lily-T and Lily-Q, two new methods for species tree inference under the multispecies coalescent. We then compare them to two frequently used methods, SVDQuartets and ASTRAL, using simulated and empirical data. Both methods generally showed improvement over SVDQuartets, and Lily-Q was superior to Lily-T for most simulation settings. The comparison to ASTRAL was more mixed—Lily-Q tended to be better than ASTRAL when the length of recombination-free loci was short, when the coalescent population parameter \(\theta \) was small, or when the internal branch lengths were longer.

由于基因组不同部分的不同进化历史，对物种进化历史的推断（通常由物种树表示）变得复杂。由于不完全谱系分选 (ILS)、基因重复和丢失以及水平基因转移等过程，基因组上的不同位点可能具有与底层物种树（以及彼此之间）不同的历史。多物种合并是在 ILS 存在的情况下对物种和基因树进行推理的常用模型。本文介绍了 Lily-T 和 Lily-Q 这两种新的多物种聚结下物种树推断方法。然后，我们使用模拟和经验数据将它们与两种常用方法 SVDQuartets 和 ASTRAL 进行比较。这两种方法通常都表现出优于 SVDQuartets 的改进，对于大多数模拟设置，Lily-Q 优于 Lily-T。与 ASTRAL 的比较更加复杂——当无重组基因座的长度较短时，Lily-Q 往往优于 ASTRAL，当聚结种群参数\(\theta \)很小，或者当内部分支长度较长时。