DISTIQUE is essentially a method for 1) defining distances based on quartets, and 2) subsampling the space of all Θ(n 4) quartets. The first aspect of DISTIQUE can be replaced by improved ways of defining distances, for example those that better handle gene tree estimation error. Co-estimation of gene trees and the species tree  is a computationally challenging problem in general. However, it is reasonable to think that a similar problem defined on quartets, and addressed using distances becomes easier, as some recent theoretical results suggest [32 , 59]. DISTIQUE provides a general way for using anchoring introduced in this paper to implement novel distance-based gene tree species tree co-estimation in a scalable fashion. Simpler approaches of taking into account gene tree uncertainty, for example weighting various quartets according to coalescent expectations, might also result in improvements. Finally, we note that DISTIQUE’s anchoring strategy can be paired with site-based ILS methods such as SVDQuartets , and more broadly for other tree inference problems.