Species tree estimation using ASTRAL: how many genes are enough?

Species tree reconstruction from genomic data is increasingly performed using methods that account for sources of gene tree discordance such as incomplete lineage sorting. One popular method for reconstructing species trees from unrooted gene tree topologies is ASTRAL. In this paper, we derive theoretical sample complexity results for the number of genes required by ASTRAL to guarantee reconstruction of the correct species tree with high probability. We also validate those theoretical bounds in a simulation study. Our results indicate that ASTRAL requires $\mathcal{O}(f^{-2} \log n)$ gene trees to reconstruct the species tree correctly with high probability where n is the number of species and f is the length of the shortest branch in the species tree. Our simulations, which are the first to test ASTRAL explicitly under the anomaly zone, show trends consistent with the theoretical bounds and also provide some practical insights on the conditions where ASTRAL works well.