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.     

Concordance analysis in mitogenomic phylogenetics

Here I advocate the utility of Bayesian concordance analysis as a mechanism for exploring the magnitude and source of phylogenetic signal in concatenated mitogenomic phylogenetic studies. While typically applied to the study of independently evolving gene trees, Bayesian concordance analysis can also be applied to linked, but individually analyzed, gene regions using a prior probability that reflects the expectation of similar phylogenetic reconstructions. For true branches in the mitogenomic tree, concordance factors should represent the number of gene regions that contain phylogenetic signal for a particular clade. As a demonstration of the application of Bayesian concordance analysis to empirical data, I analyzed two different salamander (Hynobiidae and Plethodontidae) mitogenomic data sets using a gene-based partitioning strategy. The results revealed many strongly supported clades in the concatenated trees that have high concordance factors, permitting the inference that these are robustly resolved through phylogenetic signal distributed across the mitogenome. In contrast, a number of strongly supported clades in the concatenated tree received low concordance factors, indicating that their reconstruction is either driven primarily by phylogenetic signal in a small number of gene regions, or that they are inconsistent reconstructions influenced by properties of the data that can produce inaccurate trees (e.g., compositional bias, selection, etc.). Exploration of the Bayesian joint posterior distribution of trees highlighted partitions that contribute phylogenetic information to similar clade reconstructions. This approach was particularly insightful in the hynobiid data, where different combinations of genes were identified that support alternative tree reconstructions. Concatenated analysis of these different subsets of genes highlighted through Bayesian concordance analysis produced strongly supported and contrasting trees, demonstrating the potential for inconsistency in concatenated mitogenomic phylogenetics. The overall results presented here suggest that Bayesian concordance analysis can serve as an effective exploration of the influence of different gene regions in mitogenomic (and other organellar genomic) phylogenetic studies.     

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.     

Polytomies and Bayesian phylogenetic inference

Bayesian phylogenetic analyses are now very popular in systematics and molecular evolution because they allow the use of much more realistic models than currently possible with maximum likelihood methods. There are, however, a growing number of examples in which large Bayesian posterior clade probabilities are associated with very short branch lengths and low values for non-Bayesian measures of support such as nonparametric bootstrapping. For the four-taxon case when the true tree is the star phylogeny, Bayesian analyses become increasingly unpredictable in their preference for one of the three possible resolved tree topologies as data set size increases. This leads to the prediction that hard (or near-hard) polytomies in nature will cause unpredictable behavior in Bayesian analyses, with arbitrary resolutions of the polytomy receiving very high posterior probabilities in some cases. We present a simple solution to this problem involving a reversible-jump Markov chain Monte Carlo (MCMC) algorithm that allows exploration of all of tree space, including unresolved tree topologies with one or more polytomies. The reversible-jump MCMC approach allows prior distributions to place some weight on less-resolved tree topologies, which eliminates misleadingly high posteriors associated with arbitrary resolutions of hard polytomies. Fortunately, assigning some prior probability to polytomous tree topologies does not appear to come with a significant cost in terms of the ability to assess the level of support for edges that do exist in the true tree. Methods are discussed for applying arbitrary prior distributions to tree topologies of varying resolution, and an empirical example showing evidence of polytomies is analyzed and discussed.     

Guided tree topology proposals for Bayesian phylogenetic inference

Increasingly, large data sets pose a challenge for computationally intensive phylogenetic methods such as Bayesian Markov chain Monte Carlo (MCMC). Here, we investigate the performance of common MCMC proposal distributions in terms of median and variance of run time to convergence on 11 data sets. We introduce two new Metropolized Gibbs Samplers for moving through "tree space." MCMC simulation using these new proposals shows faster average run time and dramatically improved predictability in performance, with a 20-fold reduction in the variance of the time to estimate the posterior distribution to a given accuracy. We also introduce conditional clade probabilities and demonstrate that they provide a superior means of approximating tree topology posterior probabilities from samples recorded during MCMC.     

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.     

The relative contribution of band number to phylogenetic accuracy in AFLP data sets

We examined the effect of increasing the number of sampled amplified fragment length polymorphism (AFLP) bands to reconstruct an accurate and well-supported AFLP-based phylogeny. In silico AFLP was performed using simulated DNA sequences evolving along balanced and unbalanced model trees with recent, uniform and ancient radiations and average branch lengths (from the most internal node to the tip) ranging from 0.02 to 0.05 substitutions per site. Trees were estimated by minimum evolution (ME) and maximum parsimony (MP) methods from both DNA sequences and virtual AFLP fingerprints. The comparison of the true tree with the estimated AFLP trees suggests that moderate numbers of AFLP bands are necessary to recover the correct topology with high bootstrap support values (i.e. >70%). Fewer numbers of bands are necessary for shorter tree lengths and for balanced than for unbalanced tree topologies. However, branch length estimation was rather unreliable and did not improve substantially after a certain number of bands were sampled. These results hold for different levels of genome coverage and number of taxa analysed. In silico AFLP using bacterial genomic DNA sequences recovered a well-supported tree topology that mirrored an empirical phylogeny based on a set of 31 orthologous gene sequences when as few as 263 AFLP bands were scored. These results suggest that AFLPs may be an efficient alternative to traditional DNA sequencing for accurate topology reconstruction of shallow trees when not very short ancestral branches exist.     

Gene tree distributions under the coalescent process

Under the coalescent model for population divergence, lineage sorting can cause considerable variability in gene trees generated from any given species tree. In this paper, we derive a method for computing the distribution of gene tree topologies given a bifurcating species tree for trees with an arbitrary number of taxa in the case that there is one gene sampled per species. Applications for gene tree distributions include determining exact probabilities of topological equivalence between gene trees and species trees and inferring species trees from multiple datasets. In addition, we examine the shapes of gene tree distributions and their sensitivity to changes in branch lengths, species tree shape, and tree size. The method for computing gene tree distributions is implemented in the computer program COAL.     

Estimating species trees using approximate Bayesian computation

Development of methods for estimating species trees from multilocus data is a current challenge in evolutionary biology. We propose a method for estimating the species tree topology and branch lengths using approximate Bayesian computation (ABC). The method takes as data a sample of observed rooted gene tree topologies, and then iterates through the following sequence of steps: First, a randomly selected species tree is used to compute the distribution of rooted gene tree topologies. This distribution is then compared to the observed gene topology frequencies, and if the fit between the observed and the predicted distributions is close enough, the proposed species tree is retained. Repeating this many times leads to a collection of retained species trees that are then used to form the estimate of the overall species tree. We test the performance of the method, which we call ST-ABC, using both simulated and empirical data. The simulation study examines both symmetric and asymmetric species trees over a range of branch lengths and sample sizes. The results from the simulation study show that the model performs very well, giving accurate estimates for both the topology and the branch lengths across the conditions studied, and that a sample size of 25 loci appears to be adequate for the method. Further, we apply the method to two empirical cases: a 4-taxon data set for primates and a 7-taxon data set for yeast. In both cases, we find that estimates obtained with ST-ABC agree with previous studies. The method provides efficient estimation of the species tree, and does not require sequence data, but rather the observed distribution of rooted gene topologies without branch lengths. Therefore, this method is a useful alternative to other currently available methods for species tree estimation.     

Gene tree parsimony of multilocus snake venom protein families reveals species tree conflict as a result of multiple parallel gene loss

The proliferation of gene data from multiple loci of large multigene families has been greatly facilitated by considerable recent advances in sequence generation. The evolution of such gene families, which often undergo complex histories and different rates of change, combined with increases in sequence data, pose complex problems for traditional phylogenetic analyses, and in particular, those that aim to successfully recover species relationships from gene trees. Here, we implement gene tree parsimony analyses on multicopy gene family data sets of snake venom proteins for two separate groups of taxa, incorporating Bayesian posterior distributions as a rigorous strategy to account for the uncertainty present in gene trees. Gene tree parsimony largely failed to infer species trees congruent with each other or with species phylogenies derived from mitochondrial and single-copy nuclear sequences. Analysis of four toxin gene families from a large expressed sequence tag data set from the viper genus Echis failed to produce a consistent topology, and reanalysis of a previously published gene tree parsimony data set, from the family Elapidae, suggested that species tree topologies were predominantly unsupported. We suggest that gene tree parsimony failure in the family Elapidae is likely the result of unequal and/or incomplete sampling of paralogous genes and demonstrate that multiple parallel gene losses are likely responsible for the significant species tree conflict observed in the genus Echis. These results highlight the potential for gene tree parsimony analyses to be undermined by rapidly evolving multilocus gene families under strong natural selection.     

Strange bayes indeed: uniform topological priors imply non-uniform clade priors

While Bayesian analysis has become common in phylogenetics, the effects of topological prior probabilities on tree inference have not been investigated. In Bayesian analyses, the prior probability of topologies is almost always considered equal for all possible trees, and clade support is calculated from the majority rule consensus of the approximated posterior distribution of topologies. These uniform priors on tree topologies imply non-uniform prior probabilities of clades, which are dependent on the number of taxa in a clade as well as the number of taxa in the analysis. As such, uniform topological priors do not model ignorance with respect to clades. Here, we demonstrate that Bayesian clade support, bootstrap support, and jackknife support from 17 empirical studies are significantly and positively correlated with non-uniform clade priors resulting from uniform topological priors. Further, we demonstrate that this effect disappears for bootstrap and jackknife when data sets are free from character conflict, but remains pronounced for Bayesian clade supports, regardless of tree shape. Finally, we propose the use of a Bayes factor to account for the fact that uniform topological priors do not model ignorance with respect to clade probability.     

Phylogenetic position of Salinibacter ruber based on concatenated protein alignments

A total of 22 genes from the genome of Salinibacter ruber strain M31 were selected in order to study the phylogenetic position of this species based on protein alignments. The selection of the genes was based on their essential function for the organism, dispersion within the genome, and sufficient informative length of the final alignment. For each gene, an individual phylogenetic analysis was performed and compared with the resulting tree based on the concatenation of the 22 genes, which rendered a single alignment of 10,757 homologous positions. In addition to the manually chosen genes, an automatically selected data set of 74 orthologous genes was used to reconstruct a tree based on 17,149 homologous positions. Although single genes supported different topologies, the tree topology of both concatenated data sets was shown to be identical to that previously observed based on small subunit (SSU) rRNA gene analysis, in which S. ruber was placed together with Bacteroidetes. In both concatenated data sets the bootstrap was very high, but an analysis with a gradually lower number of genes indicated that the bootstrap was greatly reduced with less than 12 genes. The results indicate that tree reconstructions based on concatenating large numbers of protein coding genes seem to produce tree topologies with similar resolution to that of the single 16S rRNA gene trees. For classification purposes, 16S rRNA gene analysis may remain as the most pragmatic approach to infer genealogic relationships.     

The Apicomplexan whole-genome phylogeny: an analysis of incongruence among gene trees

The protistan phylum Apicomplexa contains many important pathogens and is the subject of intense genome sequencing efforts. Based upon the genome sequences from seven apicomplexan species and a ciliate outgroup, we identified 268 single-copy genes suitable for phylogenetic inference. Both concatenation and consensus approaches inferred the same species tree topology. This topology is consistent with most prior conceptions of apicomplexan evolution based upon ultrastructural and developmental characters, that is, the piroplasm genera Theileria and Babesia form the sister group to the Plasmodium species, the coccidian genera Eimeria and Toxoplasma are monophyletic and are the sister group to the Plasmodium species and piroplasm genera, and Cryptosporidium forms the sister group to the above mentioned with the ciliate Tetrahymena as the outgroup. The level of incongruence among gene trees appears to be high at first glance; only 19% of the genes support the species tree, and a total of 48 different gene-tree topologies are observed. Detailed investigations suggest that the low signal-to-noise ratio in many genes may be the main source of incongruence. The probability of being consistent with the species tree increases as a function of the minimum bootstrap support observed at tree nodes for a given gene tree. Moreover, gene sequences that generate high bootstrap support are robust to the changes in alignment parameters or phylogenetic method used. However, caution should be taken in that some genes can infer a "wrong" tree with strong support because of paralogy, model violations, or other causes. The importance of examining multiple, unlinked genes that possess a strong phylogenetic signal cannot be overstated.     

Estimating species trees using multiple-allele DNA sequence data

Several techniques, such as concatenation and consensus methods, are available for combining data from multiple loci to produce a single statement of phylogenetic relationships. However, when multiple alleles are sampled from individual species, it becomes more challenging to estimate relationships at the level of species, either because concatenation becomes inappropriate due to conflicts among individual gene trees, or because the species from which multiple alleles have been sampled may not form monophyletic groups in the estimated tree. We propose a Bayesian hierarchical model to reconstruct species trees from multiple-allele, multilocus sequence data, building on a recently proposed method for estimating species trees from single allele multilocus data. A two-step Markov Chain Monte Carlo (MCMC) algorithm is adopted to estimate the posterior distribution of the species tree. The model is applied to estimate the posterior distribution of species trees for two multiple-allele datasets--yeast (Saccharomyces) and birds (Manacus-manakins). The estimates of the species trees using our method are consistent with those inferred from other methods and genetic markers, but in contrast to other species tree methods, it provides credible regions for the species tree. The Bayesian approach described here provides a powerful framework for statistical testing and integration of population genetics and phylogenetics.     

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%.      

Gene tree discordance of wild and cultivated Asian rice deciphered by genome-wide sequence comparison

Although a large number of genes are expected to correctly solve a phylogenetic relationship, inconsistent gene tree topologies have been observed. This conflicting evidence in gene tree topologies, known as gene tree discordance, becomes increasingly important as advanced sequencing technologies produce an enormous amount of sequence information for phylogenomic studies among closely related species. Here, we aim to characterize the gene tree discordance of the Asian cultivated rice Oryza sativa and its progenitor, O. rufipogon, which will be an ideal case study of gene tree discordance. Using genome and cDNA sequences of O. sativa and O. rufipogon, we have conducted the first in-depth analyses of gene tree discordance in Asian rice. Our comparison of full-length cDNA sequences of O. rufipogon with the genome sequences of the japonica and indica cultivars of O. sativa revealed that 60% of the gene trees showed a topology consistent with the expected one, whereas the remaining genes supported significantly different topologies. Moreover, the proportions of the topologies deviated significantly from expectation, suggesting at least one hybridization event between the two subgroups of O. sativa, japonica and indica. In fact, a genome-wide alignment between japonica and indica indicated that significant portions of the indica genome are derived from japonica. In addition, literature concerning the pedigree of the indica cultivar strongly supported the hybridization hypothesis. Our molecular evolutionary analyses deciphered complicated evolutionary processes in closely related species. They also demonstrated the importance of gene tree discordance in the era of high-speed DNA sequencing.     

Conditioned genome reconstruction: how to avoid choosing the conditioning genome

Genome phylogenies can be inferred from data on the presence and absence of genes across taxa. Logdet distances may be a good method, because they allow expected genome size to vary across the tree. Recently, Lake and Rivera proposed conditioned genome reconstruction (calculation of logdet distances using only those genes present in a conditioning genome) to deal with unobservable genes that are absent from every taxon of interest. We prove that their method can consistently estimate the topology for almost any choice of conditioning genome. Nevertheless, the choice of conditioning genome is important for small samples. For real bacterial genome data, different choices of conditioning genome can result in strong bootstrap support for different tree topologies. To overcome this problem, we developed supertree methods that combine information from all choices of conditioning genome. One of these methods, based on the BIONJ algorithm, performs well on simulated data and may have applications to other supertree problems. However, an analysis of 40 bacterial genomes using this method supports an incorrect clade of parasites. This is a common feature of model-based gene content methods and is due to parallel gene loss.     

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.     

The probability of a gene tree topology within a phylogenetic network with applications to hybridization detection

Gene tree topologies have proven a powerful data source for various tasks, including species tree inference and species delimitation. Consequently, methods for computing probabilities of gene trees within species trees have been developed and widely used in probabilistic inference frameworks. All these methods assume an underlying multispecies coalescent model. However, when reticulate evolutionary events such as hybridization occur, these methods are inadequate, as they do not account for such events. Methods that account for both hybridization and deep coalescence in computing the probability of a gene tree topology currently exist for very limited cases. However, no such methods exist for general cases, owing primarily to the fact that it is currently unknown how to compute the probability of a gene tree topology within the branches of a phylogenetic network. Here we present a novel method for computing the probability of gene tree topologies on phylogenetic networks and demonstrate its application to the inference of hybridization in the presence of incomplete lineage sorting. We reanalyze a Saccharomyces species data set for which multiple analyses had converged on a species tree candidate. Using our method, though, we show that an evolutionary hypothesis involving hybridization in this group has better support than one of strict divergence. A similar reanalysis on a group of three Drosophila species shows that the data is consistent with hybridization. Further, using extensive simulation studies, we demonstrate the power of gene tree topologies at obtaining accurate estimates of branch lengths and hybridization probabilities of a given phylogenetic network. Finally, we discuss identifiability issues with detecting hybridization, particularly in cases that involve extinction or incomplete sampling of taxa.     

The serine repeat antigen (SERA) gene family phylogeny in Plasmodium: the impact of GC content and reconciliation of gene and species trees

Plasmodium falciparum is the parasite responsible for the most acute form of malaria in humans. Recently, the serine repeat antigen (SERA) in P. falciparum has attracted attention as a potential vaccine and drug target, and it has been shown to be a member of a large gene family. To clarify the relationships among the numerous P. falciparum SERAs and to identify orthologs to SERA5 and SERA6 in Plasmodium species affecting rodents, gene trees were inferred from nucleotide and amino acid sequence data for 33 putative SERA homologs in seven different species. (A distance method for nucleotide sequences that is specifically designed to accommodate differing GC content yielded results that were largely compatible with the amino acid tree. Standard-distance and maximum-likelihood methods for nucleotide sequences, on the other hand, yielded gene trees that differed in important respects.) To infer the pattern of duplication, speciation, and gene loss events in the SERA gene family history, the resulting gene trees were then "reconciled" with two competing Plasmodium species tree topologies that have been identified by previous phylogenetic studies. Parsimony of reconciliation was used as a criterion for selecting a gene tree/species tree pair and provided (1) support for one of the two species trees and for the core topology of the amino acid-derived gene tree, (2) a basis for critiquing fine detail in a poorly resolved region of the gene tree, (3) a set of predicted "missing genes" in some species, (4) clarification of the relationship among the P. falciparum SERA, and (5) some information about SERA5 and SERA6 orthologs in the rodent malaria parasites. Parsimony of reconciliation and a second criterion--implied mutational pattern at two key active sites in the SERA proteins-were also seen to be useful supplements to standard "bootstrap" analysis for inferred topologies.