In this study, we basically followed the simulation procedure used in Gascuel and Steel (2014) (link). We generated pure-birth trees with n = 1,000 tips. To obtain a broad range of ACR difficulties, we used 16 values of the speciation/evolutionary rate ratio (ω) ranging from 0.2 to 8.0, which correspond to an average number of state changes per branch of 2.5 and 0.0625, respectively (Steel and Mooers 2010 ). With a high number of state changes per branch (e.g., 2.5) ACR is very difficult, especially for the tree root, whereas with a low number of changes (e.g., 0.0625) ACR becomes easy as all tips and nodes tend to have the same state value. For each value of ω, 50 trees were generated, and for each tree we simulated the evolution of 50 unique characters with 4 states, and 50 with 20 states. To ease the implementation, reproducibility and interpretation of the results, we used DNA and protein models, although the method and software are intended for unique characters. We generated 4-state data sets using Seq-Gen v1.3.2 (Rambaut and Grass 1997 ) and the HKY model (Hasegawa et al. 1985 (link)) with equilibrium frequencies of A, C, G, and T being equal to 0.2, 0.1, 0.3, and 0.4, respectively, and a transition/transversion ratio κ of 8.0. These relatively extreme values were chosen to challenge ACR when using the F81 model implemented in PastML. Likewise, we generated 20-state data sets using Seq-Gen and the JTT model (Jones et al. 1992 ) with its default amino-acid equilibrium frequencies. We thusly obtained 16 (ω values) × 50 (1,000-tip trees) × 50 (number of characters) × 2 (4-state/20-state) data sets to assess the accuracy of ACR methods. During the simulation procedure with Seq-Gen, we recorded the ancestral state of the character seen at each internal node, including the root. Thus, the “true” ancestral scenario was known. All these data sets are available from https://pastml.pasteur.fr/.