The Global LAteSt Split (GLASS)/Maximum Tree (MT) method of species tree inference, implemented in the software STEM, performs well and is statistically consistent when inferring a species tree from known gene trees. When input gene trees are estimated from DNA sequences, it can perform poorly, with possibly unrealistic sufficient conditions for statistical consistency. We propose a modification to STEM, called genX, which replaces its estimated pairwise coalescence times with randomly generated realizations from an estimated distribution of the true coalescence times. This adjusts for measurement error as described by Su, Reedy, and Carroll in 2018, or using a Bayesian approach. As with STEM, the minimum of these realizations is taken over all loci for each pairwise distance, forming a distance matrix, and the species tree is inferred using single linkage clustering. In simulations and in two empirical datasets, the new methods outperformed STEM in terms of Robinson-Foulds distance from the true species tree, though the Bayesian approach requires more computation time and is prone to convergence issues. In our simulations, overcoming some gene tree estimation error improved the performance of STEM.

MOTIVATION: Consensus methods can be used for reconstructing a species tree from several gene trees, which exhibit incompatible topologies due to incomplete lineage sorting. Motivated by the fact that there are no anomalous rooted gene trees with three taxa and no anomalous unrooted gene trees with four taxa in the multispecies coalescent model, several contemporary methods form the gene tree consensus by finding the median tree with respect to the triplet or quartet distance-i.e. estimate the species tree as the tree which minimizes the sum of triplet or quartet distances to the input gene trees. These methods reformulate the solution to the consensus problem as the solution to a recursively solved dynamic programming (DP) problem. We present an iterative, easily parallelizable approach to finding the exact median triplet tree and implement it as an open source software package that can also find suboptimal consensus trees within a specified triplet distance to the gene trees. The most time-consuming step for methods of this type is the creation of a weights array for all possible subtree bipartitions. By grouping the relevant calculations and array update operations of different bipartitions of the same subtree together, this implementation finds the exact median tree of many gene trees faster than comparable methods, has better scaling properties with respect to the number of gene trees and has a smaller memory footprint. RESULTS: RTIST (Rooted Triple Inference of Species Trees) finds the exact median triplet tree of a set of gene trees. Its runtime and memory footprints scale better than existing algorithms. RTIST can resolve all the non-unique median trees, as well as sub-optimal consensus trees within a user-specified triplet distance to the median. Although it is limited in the number of taxa (≤20), its runtime changes little when the number of gene trees is changed by several orders of magnitude. AVAILABILITY AND IMPLEMENTATION: RTIST is written in C and Python. It is freely available at https://github.com/glebzhelezov/rtist.

Post-specific diffusion network elucidates the who-saw-from-whom paths of a post on social media. A diffusion network for a specific post can reveal trustworthy and/or incentivized connections among users. Unfortunately, such a network is not observable from available information from social media platforms; hence an inference mechanism is needed.

SUMMARY: PRANC computes the Probabilities of RANked gene tree topologies under the multispecies coalescent. A ranked gene tree is a gene tree accounting for the temporal ordering of internal nodes. PRANC can also estimate the maximum likelihood (ML) species tree from a sample of ranked or unranked gene tree topologies. It estimates the ML tree with estimated branch lengths in coalescent units. AVAILABILITY AND IMPLEMENTATION: PRANC is written in C++ and freely available at github.com/anastasiiakim/PRANC. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

The method was proposed by Liu and Yu to infer a species tree topology from unrooted topological gene trees. While its statistical consistency under the multispecies coalescent model was established only for a four-taxon tree, simulations demonstrated its good performance on gene trees inferred from sequences for many taxa. Here, we prove the statistical consistency of the method for an arbitrarily large species tree. Our approach connects to a generalization of the STAR method of Liu, Pearl, and Edwards, and a previous theoretical analysis of it. We further show utilizes only the distribution of splits in the gene trees, and not their individual topologies. Finally, we discuss how multiple samples per taxon per gene should be handled for statistical consistency.

BACKGROUND: There has been increasing interest in coalescent models which admit multiple mergers of ancestral lineages; and to model hybridization and coalescence simultaneously. RESULTS: Hybrid-Lambda is a software package that simulates gene genealogies under multiple merger and Kingman's coalescent processes within species networks or species trees. Hybrid-Lambda allows different coalescent processes to be specified for different populations, and allows for time to be converted between generations and coalescent units, by specifying a population size for each population. In addition, Hybrid-Lambda can generate simulated datasets, assuming the infinitely many sites mutation model, and compute the F ST statistic. As an illustration, we apply Hybrid-Lambda to infer the time of subdivision of certain marine invertebrates under different coalescent processes. CONCLUSIONS: Hybrid-Lambda makes it possible to investigate biogeographic concordance among high fecundity species exhibiting skewed offspring distribution.

Ranked gene trees, which consider both the gene tree topology and the sequence in which gene lineages separate, can potentially provide a new source of information for use in modeling genealogies and performing inference of species trees. Recently,we have calculated the probability distribution of ranked gene trees under the standard multispecies coalescent model for the evolution of gene lineages along the branches of a fixed species tree, demonstrating the existence of anomalous ranked gene trees (ARGTs), in which a ranked gene tree that does not match the ranked species tree can have greater probability under the model than the matching ranked gene tree. Here, we fully characterize the set of unranked species tree topologies that give rise to ARGTs, showing that this set contains all species tree topologies with five or more taxa, with the exceptions of caterpillars and pseudocaterpillars. The results have implications for the use of ranked gene trees in phylogenetic inference.