simPhy-size: On this simulated dataset, we compare running time and tree accuracy across methods. Generally, all the methods we studied had similar patterns of accuracy on the simPhy-size dataset, and the mean errors of different methods tended to be within the standard error of each other (Fig. 1 a). According to a two-way ANOVA test with FDR correction  for multiple testing (n=24; see caption of Additional file 1: Table S3) with α=0.05, the error rate of DISTIQUE-8 was statistically indistinguishable from both ASTRAL and ASTRID (Additional file 1: Table S3). In the few cases where the differences seemed substantial, for example on 500 species and 1000 genes, ASTRAL tended to be the best, followed by both versions of DISTIQUE (but there were exceptions; e.g., 50 species and 1000 genes). Unlike the accuracy, running times of summary methods were quite different (Fig. 2). ASTRID was by far the fastest, followed by DISTIQUE-2 and DISTIQUE-8, and ASTRAL was the slowest. For example, with 500 species and 1000 genes, DISTIQUE-2 and DISTIQUE-8 ran in about 1.1 and 2.2 hours, while ASTRAL took 5 hours, and ASTRID took only 7.5 minutes. Fig. 1DISTIQUE versus other methods on (a) simPhy-size and (b) simPhy-ILS datasets using estimated gene trees. Boxes: (a) number of genes and (b) levels of ILS. The mean and standard error of species tree error are shown over (a) 50 and (b) 100 replicates Fig. 2Running time comparisons on the simPhy-size datasets with 1000 genes (Additinal file 1: Figure S6 has other numbers of genes). Lines show the average running times (50 replicates) in hours