ASTRAL-III: polynomial time species tree reconstruction from partially resolved gene trees

Background Evolutionary histories can be discordant across the genome, and such discordances need to be considered in reconstructing the species phylogeny. ASTRAL is one of the leading methods for inferring species trees from gene trees while accounting for gene tree discordance. ASTRAL uses dynamic programming to search for the tree that shares the maximum number of quartet topologies with input gene trees, restricting itself to a predefined set of bipartitions. Results We introduce ASTRAL-III, which substantially improves the running time of ASTRAL-II and guarantees polynomial running time as a function of both the number of species ( n ) and the number of genes ( k ). ASTRAL-III limits the bipartition constraint set ( X ) to grow at most linearly with n and k . Moreover, it handles polytomies more efficiently than ASTRAL-II, exploits similarities between gene trees better, and uses several techniques to avoid searching parts of the search space that are mathematically guaranteed not to include the optimal tree. The asymptotic running time of ASTRAL-III in the presence of polytomies is O ((nk)^1.726 D ) where D = O ( nk ) is the sum of degrees of all unique nodes in input trees. The running time improvements enable us to test whether contracting low support branches in gene trees improves the accuracy by reducing noise. In extensive simulations, we show that removing branches with very low support (e.g., below 10