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It is well known that gene trees and species trees may have different topologies. One explanation is incomplete lineage sorting, which is commonly modeled by the coalescent process. In multispecies coalescent, a gene tree topology is observed with some probability (called the gene tree probability) for a given species tree. Gene tree probability is the main tool for the program STELLS, which finds the maximum likelihood estimate of the species tree from the given gene tree topologies. However, STELLS becomes slow when data size increases. Recently, several fast species tree inference methods have been developed, which can handle large data. However, these methods often do not fully utilize the information in the gene trees.

STELLS2: fast and accurate coalescent-based maximum likelihood inference of species trees from gene tree topologies