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Inference of the evolutionary histories of species, commonly represented by aspecies tree, is complicated by the divergent evolutionary history of differentparts of the genome. Different loci on the genome can have different historiesfrom the underlying species tree (and each other) due to processes such asincomplete lineage sorting (ILS), gene duplication and loss, and horizontalgene transfer. The multispecies coalescent is a commonly used model forperforming inference on species and gene trees in the presence of ILS. Thispaper introduces Lily-T and Lily-Q, two new methods for species tree inferenceunder the multispecies coalescent. We then compare them to two frequently usedmethods, SVDQuartets and ASTRAL, using simulated and empirical data. Bothmethods generally showed improvement over SVDQuartets, and Lily-Q was superiorto 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-freeloci was short, when the coalescent population parameter {\theta} was small, orwhen the internal branch lengths were longer.

Bayesian Weighted Triplet and Quartet Methods for Species Tree Inference