  The $\text{NJ}_{st}$ method was proposed by Liu and Yu to infer a species
tree topology from unrooted topological gene trees. While its statistical
consistency under the multispecies coalescent model was established only for a
4-taxon tree, simulations demonstrated its good performance on gene trees
inferred from sequences for many taxa. Here we prove the statistical
consistency of the method for an arbitrarily large species tree. Our approach
connects $\text{NJ}_{st}$ to a generalization of the STAR method of Liu, Pearl
and Edwards, and a previous theoretical analysis of it. We further show
$\text{NJ}_{st}$ utilizes only the distribution of splits in the gene trees,
and not their individual topologies. Finally, we discuss how multiple samples
per taxon per gene should be handled for statistical consistency.
