We address the problem of rooting an unrooted species tree given a set of unrooted gene trees, under the assumption that gene trees evolve within the model species tree under the multispecies coalescent (MSC) model. Quintet Rooting (QR) is a polynomial time algorithm that was recently proposed for this problem, which is based on the theory developed by Allman, Degnan, and Rhodes that proves the identifiability of rooted 5-taxon trees from unrooted gene trees under the MSC. However, although QR had good accuracy in simulations, its statistical consistency was left as an open problem. We present QR-STAR, a variant of QR with an additional step and a different cost function, and prove that it is statistically consistent under the MSC. Moreover, we derive sample complexity bounds for QR-STAR and show that a particular variant of it based on "short quintets" has polynomial sample complexity. Finally, our simulation study under a variety of model conditions shows that QR-STAR matches or improves on the accuracy of QR. QR-STAR is available in open-source form on github.

中文翻译：

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QR-STAR：一种在聚结作用下使物种树生根的多项式时间统计一致方法。


假设基因树在多物种合并（MSC）模型下的模型物种树内进化，我们解决了给定一组无根基因树的无根物种树的生根问题。 Quintet Rooting (QR) 是最近针对该问题提出的多项式时间算法，该算法基于 Allman、Degnan 和 Rhodes 提出的理论，证明了 MSC 下有根 5 类群树与无根基因树的可识别性。然而，尽管 QR 在模拟中具有良好的准确性，但其统计一致性仍然是一个悬而未决的问题。我们提出了 QR-STAR，这是 QR 的一种变体，具有额外的步骤和不同的成本函数，并证明它在 MSC 下具有统计上的一致性。此外，我们推导了 QR-STAR 的样本复杂度界限，并表明它基于“短五重奏”的特定变体具有多项式样本复杂度。最后，我们在各种模型条件下的模拟研究表明，QR-STAR 与 QR 的准确性相匹配或有所提高。 QR-STAR 在 github 上以开源形式提供。