The estimation of species trees (phylogenies) is one of the most important problems in evolutionary biology, and recently, there has been greater appreciation of the need to estimate species trees directly rather than using gene trees as a surrogate. A Bayesian method constructed under the multispecies coalescent model can consistently estimate species trees but involves intensive computation, which can hinder its application to the phylogenetic analysis of large-scale genomic data. Many summary statistics–based approaches, such as shallowest coalescences (SC) and Global LAteSt Split (GLASS), have been developed to infer species phylogenies for multilocus data sets. In this paper, we propose 2 methods, species tree estimation using average ranks of coalescences (STAR) and species tree estimation using average coalescence times (STEAC), based on the summary statistics of coalescence times. It can be shown that the 2 methods are statistically consistent under the multispecies coalescent model. STAR uses the ranks of coalescences and is thus resistant to variable substitution rates along the branches in gene trees. A simulation study suggests that STAR consistently outperforms STEAC, SC, and GLASS when the substitution rates among lineages are highly variable. Two real genomic data sets were analyzed by the 2 methods and produced species trees that are consistent with previous results. [Coalescent model; gene tree; species tree.]

Summary: BEST implements a Bayesian hierarchical model to jointly estimate gene trees and the species tree from multilocus sequences. It provides a new option for estimating species phylogenies within the popular Bayesian phylogenetic program MrBayes. The technique of simulated annealing is adopted along with Metropolis coupling as performed in MrBayes to improve the convergence rate of the Markov Chain Monte Carlo algorithm.

Abstract. — Estimating phylogenetic relationships among closely related species can be extremely difficult when there is incongruence among gene trees and between the gene trees and the species tree. Here we show that incorporating a model of the stochastic loss of gene lineages by genetic drift into the phylogenetic estimation procedure can provide a robust estimate of species relationships, despite widespread incomplete sorting of ancestral polymorphism. This approach is applied to a group of montane Melanoplus grasshoppers for which genealogical discordance among loci and incomplete lineage sorting obscures any obvious phylogenetic relationships among species. Unlike traditional treatments where gene trees estimated using standard phylogenetic methods are implicitly equated with the species tree, with the coalescent-based approach the species tree is modeled probabilistically from the estimated gene trees. The estimated species phylogeny (the ESP) is calculated for the grasshoppers from multiple gene trees reconstructed for nuclear loci and a mitochondrial gene. This empirical application is coupled with a simulation study to explore the performance of the coalescent-based approach. Specifically, we test the accuracy of the ESP given the data based on analyses of simulated data matching the multilocus data collected in Melanoplus (i.e., data were simulated for each locus with the same number of base pairs and locus-specific mutational models). The results of the study show that ESPs can be computed using the coalescent-based approach long before reciprocal monophyly has been achieved, and that these statistical estimates are accurate. This contrasts with analyses of the empirical data collected in Melanoplus and simulated data based on concatenation of multiple loci, for which the

Abstract. — Genetic data are frequently used to delimit species, where species status is determined on the basis of an exclusivity criterium, such as reciprocal monophyly. Not only are there numerous empirical examples of incongruence between the boundaries inferred from such data compared to other sources like morphology—especially with recently derived species, but population genetic theory also clearly shows that an inevitable bias in species status results because genetic thresholds do not explicitly take into account how the timing of speciation influences patterns of genetic differentiation. This study represents a fundamental shift in how genetic data might be used to delimit species. Rather than equating gene trees with a species tree or basing species status on some genetic threshold, the relationship between the gene trees and the species history is modeled probabilistically. Here we show that the same theory that is used to calculate the probability of reciprocal monophyly can also be used to delimit species despite widespread incomplete lineage sorting. The results from a preliminary simulation study suggest that very recently derived species can be accurately identified long before the requisite time for reciprocal monophyly to be achieved following speciation. The study also indicates the importance of sampling, both with regards to loci and individuals. Withstanding a thorough investigation into the conditions under which the coalescent-based approach will be effective, namely how the timing of divergence relative to the effective population size of species affects accurate species delimitation, the results are nevertheless consistent with other recent studies (aimed at inferring species relationships), showing that despite the lack of monophyletic gene trees, a signal of species divergence persists and can

Consensus methods provide a useful strategy for combining information from a collection of gene trees. An important application of consensus methods is to combine gene trees to estimate a species tree. To investigate the theoretical properties of consensus trees that would be obtained from large numbers of loci evolving according to a basic evolutionary model, we construct consensus trees from independent gene trees that occur in proportion to gene tree probabilities derived from coalescent theory. We consider majority-rule, rooted triple (R ∗), and greedy consensus trees constructed from known gene trees, both in the asymptotic case as numbers of gene trees approach infinity and for finite numbers of genes. Our results show that for some combinations of species tree branch lengths, increasing the number of independent loci can make the majority-rule consensus tree more likely to be at least partially unresolved and the greedy consensus tree less likely to match the species tree. However, the probability that the R ∗ consensus tree has the species tree topology approaches 1 as the number of gene trees approaches infinity. Although the greedy consensus algorithm can be the quickest to converge on the correct species tree when increasing the number of gene trees, it can also be positively misleading. The majority-rule consensus tree is not a misleading estimator of the species tree topology, and the R ∗ consensus tree is a statistically consistent estimator of the species tree topology. Our results therefore suggest a method for using multiple loci to infer the species tree topology, even when it is

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Numerous simulation studies have investigated the accuracy of phylogenetic inference of gene trees under max-imum parsimony, maximum likelihood, and Bayesian techniques. The relative accuracy of species tree inference methods under simulation has received less study. The number of analytical techniques available for inferring species trees is in-creasing rapidly, and in this paper, we compare the performance of several species tree inference techniques at estimating recent species divergences using computer simulation. Simulating gene trees within species trees of different shapes and with varying tree lengths (T) and population sizes (θ), and evolving sequences on those gene trees, allows us to determine how phylogenetic accuracy changes in relation to different levels of deep coalescence and phylogenetic signal. When the probability of discordance between the gene trees and the species tree is high (i.e., T is small and/or θ is large), Bayesian species tree inference using the multispecies coalescent (BEST) outperforms other methods. The performance of all methods improves as the total length of the species tree is increased, which reflects the combined benefits of decreasing the proba-bility of discordance between species trees and gene trees and gaining more accurate estimates for gene trees. Decreasing the probability of deep coalescences by reducing θ also leads to accuracy gains for most methods. Increasing the number of loci from 10 to 100 improves accuracy under difficult demographic scenarios (i.e., coalescent units 4Ne), but 10 loci are adequate for estimating the correct species tree in cases where deep coalescence is limited or absent. In general, the

Abstract.—Analyses of the increasingly available genomic data continue to reveal the extent of hybridization and its role in the evolutionary diversification of various groups of species. We show, through extensive coalescent-based simulations of multilocus data sets on phylogenetic networks, how divergence times before and after hybridization events can result in incomplete lineage sorting with gene tree incongruence signatures identical to those exhibited by hybridization. Evolutionary analysis of such data under the assumption of a species tree model can miss all hybridization events, whereas analysis under the assumption of a species network model would grossly overestimate hybridization events. These issues necessitate a paradigm shift in evolutionary analysis under these scenarios, from a model that assumes a priori a single source of gene tree incongruence to one that integrates multiple sources in a unifying framework. We propose a framework of coalescence within the branches of a phylogenetic network and show how this framework can be used to detect hybridization despite incomplete lineage sorting. We apply the model to simulated data and show that the signature of hybridization can be revealed as long as the interval between the divergence times of the species involved in hybridization is not too small.

Abstract. — Although the power of multi-locus data in estimating species trees is apparent, it is also clear that the analytical methodologies for doing so are still maturing. For example, of the methods currently available for estimating species trees from multiocus data, the Bayesian method introduced by Liu and Pearl (2007; BEST) is the only one that provides nodal support values. Using gene sequences from five nuclear loci, we explored two analytical methods (deep coalescence and BEST) to reconstruct the species tree of the five primary Manacus OTUs: M. aurantiacus, M. candei, M. vitellinus, populations of M. manacus from west of the Andes (M. manacus (w)), and populations of M. manacus from east of the Andes (M. manacus (e)). Both BEST and deep coalescence supported a sister relationship between M. vitellinus and M. manacus (w). A lower probability tree from the BEST analysis and one of the most parsimonious deep coalescence trees also supported a sister relationship between M. candei and M. aurantiacus. Because hybrid zones connect the distributions of most Manacus species, we examined the potential influence of post-divergence gene flow on the sister relationship of parapatrically distributed M. vitellinus and M. manacus (w). An isolation-with-migration (IM) analysis found relatively high levels of gene flow between M. vitellinus and M. manacus (w). Whether the gene flow is obscuring a true sister relationship between M. manacus (w) and M. manacus (e) remained unclear, pointing to the need for more detailed models accommodating multispecies, multilocus

Abstract.—The understanding that gene trees are often in discord with each other and with the species trees that contain them has led researchers to methods that incorporate the inherent stochasticity of genetic processes in the phylogenetic estimation procedure. Recently developed methods for species-tree estimation that not only consider the retention and sorting of ancestral polymorphism but also quantify the actual probabilities of incomplete lineage sorting are expected to provide an improvement over earlier summary-statistic based approaches that discard much of the information content of gene trees. However, these new methods have yet to be tested on truly challenging evolutionary histories such as those marked by recent rapid speciation where high levels of incomplete lineage sorting and discord among gene trees predominate. Here, we test a new maximum-likelihood method that incorporates stochastic models of both nucleotide substitution and lineage sorting for species-tree estimation. Using a simulation approach, we consider a broad range of species-tree topologies under 2 scenarios representing moderate and severe incomplete lineage sorting. We show that the maximum-likelihood method results in more accurate species trees than a summary-statistic based approach, demonstrating that information contained in discordant gene trees can be effectively extracted using a full probabilistic model. Moreover, we demonstrate that the shape of the original species tree (i.e., the relative lengths of internal branches) has a significant impact on whether the species tree is estimated accurately. In the speciation histories explored here, it is