In this paper, we introduce a new coalescent-based summary method, called DISTIQUE (Distance-based Inference of Species Trees from Induced QUartet Elements). Like ASTRAL, DISTIQUE is based on quartets, but instead of directly optimizing a quartet score, it uses quartets to compute pairwise distances, which are then used as input to a distance method. The innovative aspect of DISTIQUE is its method of calculating distances. It chooses two arbitrary “anchor” species and computes the frequency of quartet trees induced by gene trees that include the two anchors as sisters. We show that these frequencies can be transformed into an asymptotically additive distance matrix; using this matrix with a consistent distance-based method (e.g., neighbor joining) gives a statistically consistent summary method. This method would generate a species tree on all species except the two anchors in Θ(n 2 k) (for n species and k gene trees). However, using multiple anchor pairs can increase accuracy and can ensure all species are included in the final tree. Various strategies for choosing anchors and combining their results are introduced, with running times ranging between Θ(n 2 k) and Θ(n 4 k).