Impact of deep coalescence on the reliability of species tree inference from different types of DNA markers in mammals

An important challenge for phylogenetic studies of closely related species is the existence of deep coalescence and gene tree heterogeneity. However, their effects can vary between species and they are often neglected in phylogenetic analyses. In addition, a practical problem in the reconstruction of shallow phylogenies is to determine the most efficient set of DNA markers for a reliable estimation. To address these questions, we conducted a multilocus simulation study using empirical values of nucleotide diversity and substitution rates obtained from a wide range of mammals and evaluated the performance of both gene tree and species tree approaches to recover the known speciation times and topological relationships. We first show that deep coalescence can be a serious problem, more than usually assumed, for the estimation of speciation times in mammals using traditional gene trees. Furthermore, we tested the performance of different sets of DNA markers in the determination of species trees using a coalescent approach. Although the best estimates of speciation times were obtained, as expected, with the use of an increasing number of nuclear loci, our results show that similar estimations can be obtained with a much lower number of genes and the incorporation of a mitochondrial marker, with its high information content. Thus, the use of the combined information of both nuclear and mitochondrial markers in a species tree framework is the most efficient option to estimate recent speciation times and, consequently, the underlying species tree.     

Estimating phylogenetic relationships despite discordant gene trees across loci: the species tree of a diverse species group of feather mites (Acari: Proctophyllodidae)

With the increased availability of multilocus sequence data, the lack of concordance of gene trees estimated for independent loci has focused attention on both the biological processes producing the discord and the methodologies used to estimate phylogenetic relationships. What has emerged is a suite of new analytical tools for phylogenetic inference--species tree approaches. In contrast to traditional phylogenetic methods that are stymied by the idiosyncrasies of gene trees, approaches for estimating species trees explicitly take into account the cause of discord among loci and, in the process, provides a direct estimate of phylogenetic history (i.e. the history of species divergence, not divergence of specific loci). We illustrate the utility of species tree estimates with an analysis of a diverse group of feather mites, the pinnatus species group (genus Proctophyllodes). Discord among four sequenced nuclear loci is consistent with theoretical expectations, given the short time separating speciation events (as evident by short internodes relative to terminal branch lengths in the trees). Nevertheless, many of the relationships are well resolved in a Bayesian estimate of the species tree; the analysis also highlights ambiguous aspects of the phylogeny that require additional loci. The broad utility of species tree approaches is discussed, and specifically, their application to groups with high speciation rates--a history of diversification with particular prevalence in host/parasite systems where species interactions can drive rapid diversification.     

The accuracy of species tree estimation under simulation: a comparison of methods

Numerous simulation studies have investigated the accuracy of phylogenetic inference of gene trees under maximum 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 increasing 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 (), 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 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 probability of discordance between species trees and gene trees and gaining more accurate estimates for gene trees. Decreasing the probability of deep coalescences by reducing 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 ≤ 4N(e)), but 10 loci are adequate for estimating the correct species tree in cases where deep coalescence is limited or absent. In general, the correlation between the phylogenetic accuracy and the posterior probability values obtained from BEST is high, although posterior probabilities are overestimated when the prior distribution for is misspecified.     

CALIBRATING DIVERGENCE TIMES ON SPECIES TREES VERSUS GENE TREES: IMPLICATIONS FOR SPECIATION HISTORY OF APHELOCOMA JAYS

Estimates of the timing of divergence are central to testing the underlying causes of speciation. Relaxed molecular clocks and fossil calibration have improved these estimates; however, these advances are implemented in the context of gene trees, which can overestimate divergence times. Here we couple recent innovations for dating speciation events with the analytical power of species trees, where multilocus data are considered in a coalescent context. Divergence times are estimated in the bird genus Aphelocoma to test whether speciation in these jays coincided with mountain uplift or glacial cycles. Gene trees and species trees show general agreement that diversification began in the Miocene amid mountain uplift. However, dates from the multilocus species tree are more recent, occurring predominately in the Pleistocene, consistent with theory that divergence times can be significantly overestimated with gene‐tree based approaches that do not correct for genetic divergence that predates speciation. In addition to coalescent stochasticity, Haldane's rule could account for some differences in timing estimates between mitochondrial DNA and nuclear genes. By incorporating a fossil calibration applied to the species tree, in addition to the process of gene lineage coalescence, the present approach provides a more biologically realistic framework for dating speciation events, and hence for testing the links between diversification and specific biogeographic and geologic events.     

Species trees from gene trees: reconstructing Bayesian posterior distributions of a species phylogeny using estimated gene tree distributions

The desire to infer the evolutionary history of a group of species should be more viable now that a considerable amount of multilocus molecular data is available. However, the current molecular phylogenetic paradigm still reconstructs gene trees to represent the species tree. Further, commonly used methods of combining data, such as the concatenation method, are known to be inconsistent in some circumstances. In this paper, we propose a Bayesian hierarchical model to estimate the phylogeny of a group of species using multiple estimated gene tree distributions, such as those that arise in a Bayesian analysis of DNA sequence data. Our model employs substitution models used in traditional phylogenetics but also uses coalescent theory to explain genealogical signals from species trees to gene trees and from gene trees to sequence data, thereby forming a complete stochastic model to estimate gene trees, species trees, ancestral population sizes, and species divergence times simultaneously. Our model is founded on the assumption that gene trees, even of unlinked loci, are correlated due to being derived from a single species tree and therefore should be estimated jointly. We apply the method to two multilocus data sets of DNA sequences. The estimates of the species tree topology and divergence times appear to be robust to the prior of the population size, whereas the estimates of effective population sizes are sensitive to the prior used in the analysis. These analyses also suggest that the model is superior to the concatenation method in fitting these data sets and thus provides a more realistic assessment of the variability in the distribution of the species tree that may have produced the molecular information at hand. Future improvements of our model and algorithm should include consideration of other factors that can cause discordance of gene trees and species trees, such as horizontal transfer or gene duplication.     

The impact of gene-tree/species-tree discordance on diversification-rate estimation

Molecular phylogenies are often used to test hypotheses about the tempo and mode of speciation and extinction. One commonly used statistic is Pybus and Harvey's γ, which measures the density of ordered internode distances on an ultrametric tree to infer earlier (negative γ) or later (positive γ) bursts of diversification. However, coalescent theory predicts that γ might be biased toward negative values (inferring early bursts of diversification) when using gene trees rather than species trees. Gene divergences predate species divergences, increasingly so at higher effective population sizes (N(e)), and proportionally more so toward the tips of the tree. Thus, gene trees will have a higher density of older nodes in many cases (particularly at higher N(e)), due to the disproportionate lengthening of terminal branches. This will yield an artifactual signature of early bursts of diversification when estimating γ from gene trees. We simulate gene trees within species trees under both Yule (pure-birth) and birth-death processes, and demonstrate support for these predictions. However, for most realistic estimates of θ in natural populations, gene trees provide relatively good estimates of γ, despite the disproportionate overestimation of younger node ages. This is corroborated with an empirical dataset of North American fence lizards (Sceloporus).     

iGLASS: an improvement to the GLASS method for estimating species trees from gene trees

Several methods have been designed to infer species trees from gene trees while taking into account gene tree/species tree discordance. Although some of these methods provide consistent species tree topology estimates under a standard model, most either do not estimate branch lengths or are computationally slow. An exception, the GLASS method of Mossel and Roch, is consistent for the species tree topology, estimates branch lengths, and is computationally fast. However, GLASS systematically overestimates divergence times, leading to biased estimates of species tree branch lengths. By assuming a multispecies coalescent model in which multiple lineages are sampled from each of two taxa at L independent loci, we derive the distribution of the waiting time until the first interspecific coalescence occurs between the two taxa, considering all loci and measuring from the divergence time. We then use the mean of this distribution to derive a correction to the GLASS estimator of pairwise divergence times. We show that our improved estimator, which we call iGLASS, consistently estimates the divergence time between a pair of taxa as the number of loci approaches infinity, and that it is an unbiased estimator of divergence times when one lineage is sampled per taxon. We also show that many commonly used clustering methods can be combined with the iGLASS estimator of pairwise divergence times to produce a consistent estimator of the species tree topology. Through simulations, we show that iGLASS can greatly reduce the bias and mean squared error in obtaining estimates of divergence times in a species tree.     

Bayesian phylogenetic inference using DNA sequences: a Markov Chain Monte Carlo Method

An improved Bayesian method is presented for estimating phylogenetic trees using DNA sequence data. The birth-death process with species sampling is used to specify the prior distribution of phylogenies and ancestral speciation times, and the posterior probabilities of phylogenies are used to estimate the maximum posterior probability (MAP) tree. Monte Carlo integration is used to integrate over the ancestral speciation times for particular trees. A Markov Chain Monte Carlo method is used to generate the set of trees with the highest posterior probabilities. Methods are described for an empirical Bayesian analysis, in which estimates of the speciation and extinction rates are used in calculating the posterior probabilities, and a hierarchical Bayesian analysis, in which these parameters are removed from the model by an additional integration. The Markov Chain Monte Carlo method avoids the requirement of our earlier method for calculating MAP trees to sum over all possible topologies (which limited the number of taxa in an analysis to about five). The methods are applied to analyze DNA sequences for nine species of primates, and the MAP tree, which is identical to a maximum-likelihood estimate of topology, has a probability of approximately 95%.      

Bayes estimation of species divergence times and ancestral population sizes using DNA sequences from multiple loci

The effective population sizes of ancestral as well as modern species are important parameters in models of population genetics and human evolution. The commonly used method for estimating ancestral population sizes, based on counting mismatches between the species tree and the inferred gene trees, is highly biased as it ignores uncertainties in gene tree reconstruction. In this article, we develop a Bayes method for simultaneous estimation of the species divergence times and current and ancestral population sizes. The method uses DNA sequence data from multiple loci and extracts information about conflicts among gene tree topologies and coalescent times to estimate ancestral population sizes. The topology of the species tree is assumed known. A Markov chain Monte Carlo algorithm is implemented to integrate over uncertain gene trees and branch lengths (or coalescence times) at each locus as well as species divergence times. The method can handle any species tree and allows different numbers of sequences at different loci. We apply the method to published noncoding DNA sequences from the human and the great apes. There are strong correlations between posterior estimates of speciation times and ancestral population sizes. With the use of an informative prior for the human-chimpanzee divergence date, the population size of the common ancestor of the two species is estimated to be approximately 20,000, with a 95% credibility interval (8000, 40,000). Our estimates, however, are affected by model assumptions as well as data quality. We suggest that reliable estimates have yet to await more data and more realistic models.     

Gene tree quality affects empirical coalescent branch length estimation

Assessing effects of gene tree error in coalescent analyses have widely ignored coalescent branch lengths (CBLs) despite their potential utility in estimating ancestral population demographics and detecting species tree anomaly zones. However, the ability of coalescent methods to obtain accurate estimates remains largely unexplored. Errors in gene trees should lead to underestimates of the true CBL, and for a given set of comparisons, longer CBLs should be more accurate. Here, we furthered our empirical understanding of how error in gene tree quality (i.e., locus informativeness and gene tree resolution) affect CBLs using four datasets comprised of ultraconserved elements (UCE) or exons for clades that exhibit wide ranges of branch lengths. For each dataset, we compared the impact of locus informativeness (assessed using number of parsimony-informative sites) and gene tree resolution on CBL estimates. Our results, in general, showed that CBLs were drastically shorter when estimates included low informative loci. Gene tree resolution also had an impact on UCE datasets, with polytomous gene trees producing longer branches than randomly resolved gene trees. However, resolution did not appear to affect CBL estimates from the more informative exon datasets. Thus, as expected, gene tree quality affects CBL estimates, though this can generally be minimized by using moderate filtering to select more informative loci and/or by allowing polytomies in gene trees. These approaches, as well as additional contributions to improve CBL estimation, should lead to CBLs that are useful for addressing evolutionary and biological questions.     

Coalescent-based species tree inference from gene tree topologies under incomplete lineage sorting by maximum likelihood

Incomplete lineage sorting can cause incongruence between the phylogenetic history of genes (the gene tree) and that of the species (the species tree), which can complicate the inference of phylogenies. In this article, I present a new coalescent-based algorithm for species tree inference with maximum likelihood. I first describe an improved method for computing the probability of a gene tree topology given a species tree, which is much faster than an existing algorithm by Degnan and Salter (2005). Based on this method, I develop a practical algorithm that takes a set of gene tree topologies and infers species trees with maximum likelihood. This algorithm searches for the best species tree by starting from initial species trees and performing heuristic search to obtain better trees with higher likelihood. This algorithm, called STELLS (which stands for Species Tree InfErence with Likelihood for Lineage Sorting), has been implemented in a program that is downloadable from the author's web page. The simulation results show that the STELLS algorithm is more accurate than an existing maximum likelihood method for many datasets, especially when there is noise in gene trees. I also show that the STELLS algorithm is efficient and can be applied to real biological datasets.     

A maximum pseudo-likelihood approach for estimating species trees under the coalescent model

Background  

Several 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.     

Identifying the rooted species tree from the distribution of unrooted gene trees under the coalescent

Gene trees are evolutionary trees representing the ancestry of genes sampled from multiple populations. Species trees represent populations of individuals—each with many genes—splitting into new populations or species. The coalescent process, which models ancestry of gene copies within populations, is often used to model the probability distribution of gene trees given a fixed species tree. This multispecies coalescent model provides a framework for phylogeneticists to infer species trees from gene trees using maximum likelihood or Bayesian approaches. Because the coalescent models a branching process over time, all trees are typically assumed to be rooted in this setting. Often, however, gene trees inferred by traditional phylogenetic methods are unrooted. We investigate probabilities of unrooted gene trees under the multispecies coalescent model. We show that when there are four species with one gene sampled per species, the distribution of unrooted gene tree topologies identifies the unrooted species tree topology and some, but not all, information in the species tree edges (branch lengths). The location of the root on the species tree is not identifiable in this situation. However, for 5 or more species with one gene sampled per species, we show that the distribution of unrooted gene tree topologies identifies the rooted species tree topology and all its internal branch lengths. The length of any pendant branch leading to a leaf of the species tree is also identifiable for any species from which more than one gene is sampled.     

Species tree estimation for the late blight pathogen, Phytophthora infestans, and close relatives

To better understand the evolutionary history of a group of organisms, an accurate estimate of the species phylogeny must be known. Traditionally, gene trees have served as a proxy for the species tree, although it was acknowledged early on that these trees represented different evolutionary processes. Discordances among gene trees and between the gene trees and the species tree are also expected in closely related species that have rapidly diverged, due to processes such as the incomplete sorting of ancestral polymorphisms. Recently, methods have been developed for the explicit estimation of species trees, using information from multilocus gene trees while accommodating heterogeneity among them. Here we have used three distinct approaches to estimate the species tree for five Phytophthora pathogens, including P. infestans, the causal agent of late blight disease in potato and tomato. Our concatenation-based "supergene" approach was unable to resolve relationships even with data from both the nuclear and mitochondrial genomes, and from multiple isolates per species. Our multispecies coalescent approach using both Bayesian and maximum likelihood methods was able to estimate a moderately supported species tree showing a close relationship among P. infestans, P. andina, and P. ipomoeae. The topology of the species tree was also identical to the dominant phylogenetic history estimated in our third approach, Bayesian concordance analysis. Our results support previous suggestions that P. andina is a hybrid species, with P. infestans representing one parental lineage. The other parental lineage is not known, but represents an independent evolutionary lineage more closely related to P. ipomoeae. While all five species likely originated in the New World, further study is needed to determine when and under what conditions this hybridization event may have occurred.     

Evaluating evolutionary history in the face of high gene tree discordance in Australian Gehyra (Reptilia: Gekkonidae)

Species tree methods have provided improvements for estimating species relationships and the timing of diversification in recent radiations by allowing for gene tree discordance. Although gene tree discordance is often observed, most discordance is attributed to incomplete lineage sorting rather than other biological phenomena, and the causes of discordance are rarely investigated. We use species trees from multi-locus data to estimate the species relationships, evolutionary history and timing of diversification among Australian Gehyra—a group renowned for taxonomic uncertainty and showing a large degree of gene tree discordance. We find support for a recent Asian origin and two major clades: a tropically adapted clade and an arid adapted clade, with some exceptions, but no support for allopatric speciation driven by chromosomal rearrangement in the group. Bayesian concordance analysis revealed high gene tree discordance and comparisons of Robinson–Foulds distances showed that discordance between gene trees was significantly higher than that generated by topological uncertainty within each gene. Analysis of gene tree discordance and incomplete taxon sampling revealed that gene tree discordance was high whether terminal taxon or gene sampling was maximized, indicating discordance is due to biological processes, which may be important in contributing to gene tree discordance in many recently diversified organisms.     

Biologically feasible gene trees,reconciliation maps and informative triples

Background

The history of gene families—which are equivalent to event-labeled gene trees—can be reconstructed from empirically estimated evolutionary event-relations containing pairs of orthologous, paralogous or xenologous genes. The question then arises as whether inferred event-labeled gene trees are biologically feasible, that is, if there is a possible true history that would explain a given gene tree. In practice, this problem is boiled down to finding a reconciliation map—also known as DTL-scenario—between the event-labeled gene trees and a (possibly unknown) species tree.

Results

In this contribution, we first characterize whether there is a valid reconciliation map for binary event-labeled gene trees T that contain speciation, duplication and horizontal gene transfer events and some unknown species tree S in terms of “informative” triples that are displayed in T and provide information of the topology of S. These informative triples are used to infer the unknown species tree S for T. We obtain a similar result for non-binary gene trees. To this end, however, the reconciliation map needs to be further restricted. We provide a polynomial-time algorithm to decide whether there is a species tree for a given event-labeled gene tree, and in the positive case, to construct the species tree and the respective (restricted) reconciliation map. However, informative triples as well as DTL-scenarios have their limitations when they are used to explain the biological feasibility of gene trees. While reconciliation maps imply biological feasibility, we show that the converse is not true in general. Moreover, we show that informative triples neither provide enough information to characterize “relaxed” DTL-scenarios nor non-restricted reconciliation maps for non-binary biologically feasible gene trees.

     

A simple algorithm to infer gene duplication and speciation events on a gene tree

MOTIVATION: When analyzing protein sequences using sequence similarity searches, orthologous sequences (that diverged by speciation) are more reliable predictors of a new protein's function than paralogous sequences (that diverged by gene duplication), because duplication enables functional diversification. The utility of phylogenetic information in high-throughput genome annotation ('phylogenomics') is widely recognized, but existing approaches are either manual or indirect (e.g. not based on phylogenetic trees). Our goal is to automate phylogenomics using explicit phylogenetic inference. A necessary component is an algorithm to infer speciation and duplication events in a given gene tree. RESULTS: We give an algorithm to infer speciation and duplication events on a gene tree by comparison to a trusted species tree. This algorithm has a worst-case running time of O(n(2)) which is inferior to two previous algorithms that are approximately O(n) for a gene tree of sequences. However, our algorithm is extremely simple, and its asymptotic worst case behavior is only realized on pathological data sets. We show empirically, using 1750 gene trees constructed from the Pfam protein family database, that it appears to be a practical (and often superior) algorithm for analyzing real gene trees. AVAILABILITY: http://www.genetics.wustl.edu/eddy/forester.     

Coalescent time distributions in trees of arbitrary size

The relationship between speciation times and the corresponding times of gene divergence is of interest in phylogenetic inference as a means of understanding the past evolutionary dynamics of populations and of estimating the timing of speciation events. It has long been recognized that gene divergence times might substantially pre-date speciation events. Although the distribution of the difference between these has previously been studied for the case of two populations, this distribution has not been explicitly computed for larger species phylogenies. Here we derive a simple method for computing this distribution for trees of arbitrary size. A two-stage procedure is proposed which (i) considers the probability distribution of the time from the speciation event at the root of the species tree to the gene coalescent time conditionally on the number of gene lineages available at the root; and (ii) calculates the probability mass function for the number of gene lineages at the root. This two-stage approach dramatically simplifies numerical analysis, because in the first step the conditional distribution does not depend on an underlying species tree, while in the second step the pattern of gene coalescence prior to the species tree root is irrelevant. In addition, the algorithm provides intuition concerning the properties of the distribution with respect to the various features of the underlying species tree. The methodology is complemented by developing probabilistic formulae and software, written in R. The method and software are tested on five-taxon species trees with varying levels of symmetry. The examples demonstrate that more symmetric species trees tend to have larger mean coalescent times and are more likely to have a unimodal gamma-like distribution with a long right tail, while asymmetric trees tend to have smaller mean coalescent times with an exponential-like distribution. In addition, species trees with longer branches generally have shorter mean coalescent times, with branches closest to the root of the tree being most influential.     

Species trees for the tree swallows (Genus Tachycineta): An alternative phylogenetic hypothesis to the mitochondrial gene tree

The New World swallow genus Tachycineta comprises nine species that collectively have a wide geographic distribution and remarkable variation both within- and among-species in ecologically important traits. Existing phylogenetic hypotheses for Tachycineta are based on mitochondrial DNA sequences, thus they provide estimates of a single gene tree. In this study we sequenced multiple individuals from each species at 16 nuclear intron loci. We used gene concatenated approaches (Bayesian and maximum likelihood) as well as coalescent-based species tree inference to reconstruct phylogenetic relationships of the genus. We examined the concordance and conflict between the nuclear and mitochondrial trees and between concatenated and coalescent-based inferences. Our results provide an alternative phylogenetic hypothesis to the existing mitochondrial DNA estimate of phylogeny. This new hypothesis provides a more accurate framework in which to explore trait evolution and examine the evolution of the mitochondrial genome in this group.