Data from: QR-STAR: A polynomial-time statistically consistent method for rooting species trees under the coalescent

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.