Discordance of species trees with their most likely gene trees

Because of the stochastic way in which lineages sort during speciation, gene trees may differ in topology from each other and from species trees. Surprisingly, assuming that genetic lineages follow a coalescent model of within-species evolution, we find that for any species tree topology with five or more species, there exist branch lengths for which gene tree discordance is so common that the most likely gene tree topology to evolve along the branches of a species tree differs from the species phylogeny. This counterintuitive result implies that in combining data on multiple loci, the straightforward procedure of using the most frequently observed gene tree topology as an estimate of the species tree topology can be asymptotically guaranteed to produce an incorrect estimate. We conclude with suggestions that can aid in overcoming this new obstacle to accurate genomic inference of species phylogenies.     

Estimating species trees from unrooted gene trees

In this study, we develop a distance method for inferring unrooted species trees from a collection of unrooted gene trees. The species tree is estimated by the neighbor joining (NJ) tree built from a distance matrix in which the distance between two species is defined as the average number of internodes between two species across gene trees, that is, average gene-tree internode distance. The distance method is named NJ(st) to distinguish it from the original NJ method. Under the coalescent model, we show that if gene trees are known or estimated correctly, the NJ(st) method is statistically consistent in estimating unrooted species trees. The simulation results suggest that NJ(st) and STAR (another coalescence-based method for inferring species trees) perform almost equally well in estimating topologies of species trees, whereas the Bayesian coalescence-based method, BEST, outperforms both NJ(st) and STAR. Unlike BEST and STAR, the NJ(st) method can take unrooted gene trees to infer species trees without using an outgroup. In addition, the NJ(st) method can handle missing data and is thus useful in phylogenomic studies in which data sets often contain missing loci for some individuals.     

Relationships between gene trees and species trees

It is well known that a phylogenetic tree (gene tree) constructed from DNA sequences for a genetic locus does not necessarily agree with the tree that represents the actual evolutionary pathway of the species involved (species tree). One of the important factors that cause this difference is genetic polymorphism in the ancestral species. Under the assumption of neutral mutations, this problem can be studied by evaluating the probability (P) that a gene tree has the same topology as that of the species tree. When one gene (allele) is used from each of the species involved, the probability can be expressed as a simple function of Ti = ti/(2N), where ti is the evolutionary time measured in generations for the ith internodal branch of the species tree and N is the effective population size. When any of the Ti's is less than 1, the probability P becomes considerably less than 1.0. This probability cannot be substantially increased by increasing the number of alleles sampled from a locus. To increase the probability, one has to use DNA sequences from many different loci that have evolved independently of each other.      

From gene trees to species trees II: species tree inference by minimizing deep coalescence events

When gene copies are sampled from various species, the resulting gene tree might disagree with the containing species tree. The primary causes of gene tree and species tree discord include incomplete lineage sorting, horizontal gene transfer, and gene duplication and loss. Each of these events yields a different parsimony criterion for inferring the (containing) species tree from gene trees. With incomplete lineage sorting, species tree inference is to find the tree minimizing extra gene lineages that had to coexist along species lineages; with gene duplication, it becomes to find the tree minimizing gene duplications and/or losses. In this paper, we present the following results: 1) The deep coalescence cost is equal to the number of gene losses minus two times the gene duplication cost in the reconciliation of a uniquely leaf labeled gene tree and a species tree. The deep coalescence cost can be computed in linear time for any arbitrary gene tree and species tree. 2) The deep coalescence cost is always not less than the gene duplication cost in the reconciliation of an arbitrary gene tree and a species tree. 3) Species tree inference by minimizing deep coalescence events is NP-hard.     

Coalescent histories for discordant gene trees and species trees

Given a gene tree and a species tree, a coalescent history is a list of the branches of the species tree on which coalescences in the gene tree take place. Each pair consisting of a gene tree topology and a species tree topology has some number of possible coalescent histories. Here we show that, for each n≥7, there exist a species tree topology S and a gene tree topology G≠S, both with n leaves, for which the number of coalescent histories exceeds the corresponding number of coalescent histories when the species tree topology is S and the gene tree topology is also S. This result has the interpretation that the gene tree topology G discordant with the species tree topology S can be produced by the evolutionary process in more ways than can the gene tree topology that matches the species tree topology, providing further insight into the surprising combinatorial properties of gene trees that arise from their joint consideration with species trees.     

Delimiting species without monophyletic gene trees

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 be extracted. Using an explicit model-based approach also avoids two primary problems with species delimitation that result when genetic thresholds are applied with genetic data -- the inherent biases in species detection arising from when and how speciation occurred, and failure to take into account the high stochastic variance of genetic processes. Both the utility and sensitivities of the coalescent-based approach outlined here are discussed; most notably, a model-based approach is essential for determining whether incompletely sorted gene lineages are (or are not) consistent with separate species lineages, and such inferences require accurate model parameterization (i.e., a range of realistic effective population sizes relative to potential times of divergence for the purported species). It is the goal (and motivation of this study) that genetic data might be used effectively as a source of complementation to other sources of data for diagnosing species, as opposed to the exclusion of other evidence for species delimitation, which will require an explicit consideration of the effects of the temporal dynamic of lineage splitting on genetic data.     

The probability of topological concordance of gene trees and species trees

The concordance of gene trees and species trees is reconsidered in detail, allowing for samples of arbitrary size to be taken from the species. A sense of concordance for gene tree and species tree topologies is clarified, such that if the "collapsed gene tree" produced by a gene tree has the same topology as the species tree, the gene tree is said to be topologically concordant with the species tree. The term speciodendric is introduced to refer to genes whose trees are topologically concordant with species trees. For a given three-species topology, probabilities of each of the three possible collapsed gene tree topologies are given, as are probabilities of monophyletic concordance and concordance in the sense of N. Takahata (1989), Genetics 122, 957-966. Increasing the sample size is found to increase the probability of topological concordance, but a limit exists on how much the topological concordance probability can be increased. Suggested sample sizes beyond which this probability can be increased only minimally are given. The results are discussed in terms of implications for molecular studies of phylogenetics and speciation.     

Extracting species trees from complex gene trees: reconciled trees and vertebrate phylogeny

Paralogy is a pervasive problem in trying to use nuclear gene sequences to infer species phylogenies. One strategy for dealing with this problem is to infer species phylogenies from gene trees using reconciled trees, rather than directly from the sequences themselves. In this approach, the optimal species tree is the tree that requires the fewest gene duplications to be invoked. Because reconciled trees can identify orthologous from paralogous sequences, there is no need to do this prior to the analysis. Multiple gene trees can be analyzed simultaneously; however, the problem of nonuniform gene sampling raises practical problems which are discussed. In this paper the technique is applied to phylogenies for nine vertebrate genes (aldolase, alpha-fetoprotein, lactate dehydrogenase, prolactin, rhodopsin, trypsinogen, tyrosinase, vassopressin, and Wnt-7). The resulting species tree shows much similarity with currently accepted vertebrate relationships.     

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.     

Enumeration of compact coalescent histories for matching gene trees and species trees

Journal of Mathematical Biology - Compact coalescent histories are combinatorial structures that describe for a given gene tree G and species tree S possibilities for the numbers of coalescences of...     

Discordance of species trees with their most likely gene trees: the case of five taxa

Under a coalescent model for within-species evolution, gene trees may differ from species trees to such an extent that the gene tree topology most likely to evolve along the branches of a species tree can disagree with the species tree topology. Gene tree topologies that are more likely to be produced than the topology that matches that of the species tree are termed anomalous, and the region of branch-length space that gives rise to anomalous gene trees (AGTs) is the anomaly zone. We examine the occurrence of anomalous gene trees for the case of five taxa, the smallest number of taxa for which every species tree topology has a nonempty anomaly zone. Considering all sets of branch lengths that give rise to anomalous gene trees, the largest value possible for the smallest branch length in the species tree is greater in the five-taxon case (0.1934 coalescent time units) than in the previously studied case of four taxa (0.1568). The five-taxon case demonstrates the existence of three phenomena that do not occur in the four-taxon case. First, anomalous gene trees can have the same unlabeled topology as the species tree. Second, the anomaly zone does not necessarily enclose a ball centered at the origin in branch-length space, in which all branches are short. Third, as a branch length increases, it is possible for the number of AGTs to increase rather than decrease or remain constant. These results, which help to describe how the properties of anomalous gene trees increase in complexity as the number of taxa increases, will be useful in formulating strategies for evading the problem of anomalous gene trees during species tree inference from multilocus data.     

The concordance of gene trees and species trees at two linked loci

The gene genealogies of two linked loci in three species are analyzed using a series of Markov chain models. We calculate the probability that the gene tree of one locus is concordant with the species tree, given that the gene tree of the other locus is concordant. We define a threshold value of the recombination rate, r*, to be the rate for which the difference between the conditional probability of concordance and its asymptotic value is reduced to 5% of the initial difference. We find that, although r* depends in a complicated way on the times of speciation and effective population sizes, it is always relatively small, <10/N4, where N4 is the effective size of the species represented by the internal branch of the species tree. Consequently, the concordance of gene trees of neutral loci with the species tree is expected to be on roughly the same length scale on the chromosome as the extent of significant linkage disequilibrium within species unless the effective size of contemporary populations is very different from the effective sizes of their ancestral populations. Both balancing selection and selective sweeps can result in much longer genomic regions having concordant gene trees.     

Using phylogeographic analyses of gene trees to test species status and processes

A gene tree is an evolutionary reconstruction of the genealogical history of the genetic variation found in a sample of homologous genes or DNA regions that have experienced little or no recombination. Gene trees have the potential of straddling the interface between intra- and interspecific evolution. It is precisely at this interface that the process of speciation occurs, and gene trees can therefore be used as a powerful tool to probe this interface. One application is to infer species status. The cohesion species is defined as an evolutionary lineage or set of lineages with genetic exchangeability and/or ecological interchangeability. This species concept can be phrased in terms of null hypotheses that can be tested rigorously and objectively by using gene trees. First, an overlay of geography upon the gene tree is used to test the null hypothesis that the sample is from a single evolutionary lineage. This phase of testing can indicate that the sampled organisms are indeed from a single lineage and therefore a single cohesion species. In other cases, this null hypothesis is not rejected due to a lack of power or inadequate sampling. Alternatively, this null hypothesis can be rejected because two or more lineages are in the sample. The test can identify lineages even when hybridization and lineage sorting occur. Only when this null hypothesis is rejected is there the potential for more than one cohesion species. Although all cohesion species are evolutionary lineages, not all evolutionary lineages are cohesion species. Therefore, if the first null hypothesis is rejected, a second null hypothesis is tested that all lineages are genetically exchangeable and/or ecologically interchangeable. This second test is accomplished by direct contrasts of previously identified lineages or by overlaying reproductive and/or ecological data upon the gene tree and testing for significant transitions that are concordant with the previously identified lineages. Only when this second null hypothesis is rejected is a lineage elevated to the status of cohesion species. By using gene trees in this manner, species can be identified with objective, a priori criteria with an inference procedure that automatically yields much insight into the process of speciation. When one or more of the null hypotheses cannot be rejected, this procedure also provides specific guidance for future work that will be needed to judge species status.     

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.     

TREEasy: An automated workflow to infer gene trees,species trees,and phylogenetic networks from multilocus data

Multilocus genomic data sets can be used to infer a rich set of information about the evolutionary history of a lineage, including gene trees, species trees, and phylogenetic networks. However, user‐friendly tools to run such integrated analyses are lacking, and workflows often require tedious reformatting and handling time to shepherd data through a series of individual programs. Here, we present a tool written in Python—TREEasy—that performs automated sequence alignment (with MAFFT), gene tree inference (with IQ‐Tree), species inference from concatenated data (with IQ‐Tree and RaxML‐NG), species tree inference from gene trees (with ASTRAL, MP‐EST, and STELLS2), and phylogenetic network inference (with SNaQ and PhyloNet). The tool only requires FASTA files and nine parameters as inputs. The tool can be run as command line or through a Graphical User Interface (GUI). As examples, we reproduced a recent analysis of staghorn coral evolution, and performed a new analysis on the evolution of the “WGD clade” of yeast. The latter revealed novel patterns that were not identified by previous analyses. TREEasy represents a reliable and simple tool to accelerate research in systematic biology ( https://github.com/MaoYafei/TREEasy ).     

Subdivision in an ancestral species creates asymmetry in gene trees

We consider gene trees in three species for which the species tree is known. We show that population subdivision in ancestral species can lead to asymmetry in the frequencies of the two gene trees not concordant with the species tree and, if subdivision is extreme, cause the one of the nonconcordant gene trees to be more probable than the concordant gene tree. Although published data for the human-chimp-gorilla clade and for three species of Drosophila show asymmetry consistent with our model, sequencing error could also account for observed patterns. We show that substantial levels of persistent ancestral subdivision are needed to account for the observed levels of asymmetry found in these two studies.     

AUGIST: inferring species trees while accommodating gene tree uncertainty

SUMMARY: AUGIST (accomodating uncertainty in genealogies while inferring species tress) is a new software package for inferring species trees while accommodating uncertainty in gene genealogies. It is written for the Mesquite software system and provides sampling procedures to incorporate uncertainty in gene tree reconstruction while providing confidence estimates for inferred species trees. AVAILABILITY: http://www.lycaenid.org/augist/     

The probability distribution of ranked gene trees on a species tree

The properties of random gene tree topologies have recently been studied under a coalescent model that treats a species tree as a fixed parameter. Here we develop the analogous theory for random ranked gene tree topologies, in which both the topology and the sequence of coalescences for a random gene tree are considered. We derive the probability distribution of ranked gene tree topologies conditional on a fixed species tree. We then show that similar to the unranked case, ranked gene trees that do not match either the ranking or the topology of the species tree can have greater probability than the matching ranked gene tree.     

Tree reconciliation: reconstruction of species evolution by phylogenetic gene trees

It is well known that phylogenetic trees derived from different protein families are often incongruent. This is explained by mapping errors and by the essential processes of gene duplication, loss, and horizontal transfer. Therefore, the problem is to derive a "consensus" tree best fitting the given set of gene trees. This work presents a new method of deriving this tree. The method is different from the existing ones, since it considers not only the topology of the initial gene trees, but also the reliability of their branches. Thereby one can explicitly take into account the possible errors in the gene trees caused by the absence of reliable models of sequence evolution, by uneven evolution of different gene families and taxonomic groups, etc.