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Rooted species trees are used in several downstream applications of phylogenetics. Most species tree estimation methods produce unrooted trees and additional methods are then used to root these unrooted trees. Recently, Quintet Rooting (QR) (Tabatabaee et al., ISMB and Bioinformatics 2022), a polynomial-time method for rooting an unrooted species tree given unrooted gene trees under the multispecies coalescent, was introduced. QR, which is based on a proof of identifiability of rooted 5-taxon trees in the presence of incomplete lineage sorting, was shown to have good accuracy, improving over other methods for rooting species trees when incomplete lineage sorting was the only cause of gene tree discordance, except when gene tree estimation error was very high. However, the statistical consistency of QR was left as an open question. Here, we present QR-STAR, a polynomial-time variant of QR that has an additional step for determining the rooted shape of each quintet tree. We prove that QR-STAR is statistically consistent under the multispecies coalescent model, and our simulation study shows that QR-STAR matches or improves on the accuracy of QR. QR-STAR is available in open source form at https://github.com/ytabatabaee/Quintet-Rooting. 

Abstract The Green Bank 820 MHz pulsar survey covers ≃173 deg²in the Cygnus X region of the Galaxy, centered onl= 84.°5 andb= 1.°5. Significant star formation is present in this region, and lines of sight pass through three arms of the Galaxy (Orion–Cygnus, Perseus, and an outer arm). Using the Green Bank Telescope, we recorded 200 MHz of bandwidth for 4.5 minutes at 81.92μs resolution for each of 3457 observed survey pointings during 2016 and 2017, covering about two-thirds of the total area. We searched these data for pulsars and report the discovery of six new pulsars—PSRs J2016+3820, J2016+4231, J2019+3810, J2035+3538, J2035+3655, and J2041+4551—and the codiscovery of PSR J2057+4701. PSR J2035+3655 is in a short (4.5 hr) binary orbit; we report the full binary solution and weakly constrain the mass of the pulsar via a marginal (2σ) detection of the Shapiro delay. We also searched the survey data for known pulsars to estimate the survey’s sensitivity and measured 820 MHz pulse widths and flux density for 20 detected sources. For sources that were also detected in the Green Bank North Celestial Cap survey at 350 MHz, we measure scattering parameters and compare to expectations for the region. With these results, we revisit the population estimates that motivated this survey and consider the impact of the survey’s yield on their underlying models. We note an apparent underestimate in dispersion measure predictions from typical Galactic electron density models in the survey region, and discuss future observation strategies.