BackgroundSeveral phylogenetic approaches have been developed to estimate species trees from collections of gene trees. However, maximum likelihood approaches for estimating species trees under the coalescent model are limited. Although the likelihood of a species tree under the multispecies coalescent model has already been derived by Rannala and Yang, it can be shown that the maximum likelihood estimate (MLE) of the species tree (topology, branch lengths, and population sizes) from gene trees under this formula does not exist. In this paper, we develop a pseudo-likelihood function of the species tree to obtain maximum pseudo-likelihood estimates (MPE) of species trees, with branch lengths of the species tree in coalescent units.ResultsWe show that the MPE of the species tree is statistically consistent as the number M of genes goes to infinity. In addition, the probability that the MPE of the species tree matches the true species tree converges to 1 at rate O(M -1). The simulation results confirm that the maximum pseudo-likelihood approach is statistically consistent even when the species tree is in the anomaly zone. We applied our method, Maximum Pseudo-likelihood for Estimating Species Trees (MP-EST) to a mammal dataset. The four major clades found in the MP-EST tree are consistent with those in the Bayesian concatenation tree. The bootstrap supports for the species tree estimated by the MP-EST method are more reasonable than the posterior probability supports given by the Bayesian concatenation method in reflecting the level of uncertainty in gene trees and controversies over the relationship of four major groups of placental mammals.ConclusionsMP-EST can consistently estimate the topology and branch lengths (in coalescent units) of the species tree. Although the pseudo-likelihood is derived from coalescent theory, and assumes no gene flow or horizontal gene transfer (HGT), the MP-EST method is robust to a small amount of HGT in the dataset. In addition, increasing the number of genes does not increase the computational time substantially. The MP-EST method is fast for analyzing datasets that involve a large number of genes but a moderate number of species.

The molecular era has fundamentally reshaped our knowledge of the evolution and diversification of angiosperms. One outstanding question is the phylogenetic placement of Amborella trichopoda Baill., commonly thought to represent the first lineage of extant angiosperms. Here, we leverage publicly available data and provide a broad coalescent-based species tree estimation of 45 seed plants. By incorporating 310 nuclear genes, our coalescent analyses strongly support a clade containing Amborella plus water lilies (i.e., Nymphaeales) that is sister to all other angiosperms across different nucleotide rate partitions. Our results also show that commonly applied concatenation methods produce strongly supported, but incongruent placements of Amborella: slow-evolving nucleotide sites corroborate results from coalescent analyses, whereas fast-evolving sites place Amborella alone as the first lineage of extant angiosperms. We further explored the performance of coalescent versus concatenation methods using nucleotide sequences simulated on (i) the two alternate placements of Amborella with branch lengths and substitution model parameters estimated from each of the 310 nuclear genes and (ii) three hypothetical species trees that are topologically identical except with respect to the degree of deep coalescence and branch lengths. Our results collectively suggest that the Amborella alone placement inferred using concatenation methods is likely misled by fast-evolving sites. This appears to be exacerbated by the combination of long branches in stem group angiosperms, Amborella, and Nymphaeales with the short internal branch separating Amborella and Nymphaeales. In contrast, coalescent methods appear to be more robust to elevated substitution rates.

Fast detection of cellular thiols in aqueous medium was achieved using a newly developed fluorescence probe (see picture). Based on this probe, a high-throughput fluorescence assay for glutathione reductase was developed.