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

Abstract

Motivation: 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. Results: In this paper, we present an algorithm (called STELLS2) for computing the gene tree probability more efficiently than the original STELLS. The key idea of STELLS2 is taking some'shortcuts' during the computation and computing the gene tree probability approximately. We apply the STELLS2 algorithm in the species tree inference approach in the original STELLS, which leads to a new maximum likelihood species tree inference method (also called STELLS2). Through simulation we demonstrate that the gene tree probabilities computed by STELLS2 and STELLS have strong correlation. We show that STELLS2 is almost as accurate in species tree inference as STELLS. Also STELLS2 is usually more accurate than several existing methods when there is one allele per species, although STELLS2 is slower than these methods. STELLS2 outperforms these methods significantly when there are multiple alleles per species. Availability and Implementation: The program STELLS2 is available for download at: https://github.com/yufengwudcs/STELLS2