On the distributions of bootstrap support and posterior distributions for a star tree

Several authors have recently noted that when data are generated from a star topology, posterior probabilities can often be very large, even with arbitrarily large sequence lengths. This is counter to intuition, which suggests convergence to the limit of equal probability for each topology. Here the limiting distributions of bootstrap support and posterior probabilities are obtained for a four-taxon star tree. Theoretical results are given, providing confirmation that this counterintuitive phenomenon holds for both posterior probabilities and bootstrap support. For large samples the limiting results for posterior probabilities are the same regardless of the prior. With equal-length terminal edges, the limiting distribution is similar but not the same across different choices for the lengths of the edges. In contrast to previous results, the case of unequal lengths of terminal edges is considered. With two long edges, the posterior probability of the tree with long edges together tends to be much larger. Using the neighbor-joining algorithm, with equal edge lengths, the distribution of bootstrap support tends to be qualitatively comparable to posterior probabilities. As with posterior probabilities, when two of the edges are long, bootstrap support for the tree with long branches together tends to be large. The bias is less pronounced, however, as the distribution of bootstrap support gets close to uniform for this tree, whereas posterior probabilities are much more likely to be large. Our findings for maximum likelihood estimation are based entirely on simulation and in contrast suggest that bootstrap support tends to be fairly constant across edge-length choices.     

Testing congruence in phylogenomic analysis

Phylogenomic analyses of large sets of genes or proteins have the potential to revolutionize our understanding of the tree of life. However, problems arise because estimated phylogenies from individual loci often differ because of different histories, systematic bias, or stochastic error. We have developed Concaterpillar, a hierarchical clustering method based on likelihood-ratio testing that identifies congruent loci for phylogenomic analysis. Concaterpillar also includes a test for shared relative evolutionary rates between genes indicating whether they should be analyzed separately or by concatenation. In simulation studies, the performance of this method is excellent when a multiple comparison correction is applied. We analyzed a phylogenomic data set of 60 translational protein sequences from the major supergroups of eukaryotes and identified three congruent subsets of proteins. Analysis of the largest set indicates improved congruence relative to the full data set and produced a phylogeny with stronger support for five eukaryote supergroups including the Opisthokonts, the Plantae, the stramenopiles + Apicomplexa (chromalveolates), the Amoebozoa, and the Excavata. In contrast, the phylogeny of the second largest set indicates a close relationship between stramenopiles and red algae, to the exclusion of alveolates, suggesting gene transfer from the red algal secondary symbiont to the ancestral stramenopile host nucleus during the origin of their chloroplast. Investigating phylogenomic data sets for conflicting signals has the potential to both improve phylogenetic accuracy and inform our understanding of genome evolution.     

A class frequency mixture model that adjusts for site-specific amino acid frequencies and improves inference of protein phylogeny

Background  

Widely used substitution models for proteins, such as the Jones-Taylor-Thornton (JTT) or Whelan and Goldman (WAG) models, are based on empirical amino acid interchange matrices estimated from databases of protein alignments that incorporate the average amino acid frequencies of the data set under examination (e.g JTT + F). Variation in the evolutionary process between sites is typically modelled by a rates-across-sites distribution such as the gamma (Γ) distribution. However, sites in proteins also vary in the kinds of amino acid interchanges that are favoured, a feature that is ignored by standard empirical substitution matrices. Here we examine the degree to which the pattern of evolution at sites differs from that expected based on empirical amino acid substitution models and evaluate the impact of these deviations on phylogenetic estimation.     

Likelihood, parsimony, and heterogeneous evolution

Evolutionary rates vary among sites and across the phylogenetic tree (heterotachy). A recent analysis suggested that parsimony can be better than standard likelihood at recovering the true tree given heterotachy. The authors recommended that results from parsimony, which they consider to be nonparametric, be reported alongside likelihood results. They also proposed a mixture model, which was inconsistent but better than either parsimony or standard likelihood under heterotachy. We show that their main conclusion is limited to a special case for the type of model they study. Their mixture model was inconsistent because it was incorrectly implemented. A useful nonparametric model should perform well over a wide range of possible evolutionary models, but parsimony does not have this property. Likelihood-based methods are therefore the best way to deal with heterotachy.     

Biases in Phylogenetic Estimation Can Be Caused by Random Sequence Segments

We consider the effects of fully or partially random sequences on the estimation of four-taxon phylogenies. Fully or partially random sequences occur when whole subsets of sequences or some sites for subsets of sequences are independent of sequence data for the other taxa. Random sequences can be a consequence of misalignment or because sites evolve at very fast rates in some portions of a tree, a situation that occurs especially in analyses involving deep divergence times. One might reasonably speculate that random sites will only add noise to the estimation of a phylogeny. We show that in the case that a random sequence is added to a three-taxa alignment, it is more likely to be a neighbor of the sequence corresponding to the longest branch in the three-taxon tree. Surprisingly, when only about half of the sites show randomness, a long-branch-repels form of small sample bias occurs, and when a minority of sites show randomness this becomes a long-branch-attraction bias again. The most serious bias, one that does not vanish with increasing sequence length, occurs when more than one sequence is partially random. If there is a large amount of overlap in the random sites for two sequences, those two sequences will be attracted to each other; otherwise, they will repel each other. Random sequences or sites can, therefore, cause complicated biases in phylogenetic inference. We suggest performing analyses with and without potentially saturated sequences and/or misaligned sites, to check that these biases are not affecting the inferred branching pattern.[Reviewing Editor: Dr. J. Rasmus Nielson]     

Testing for differences in rates-across-sites distributions in phylogenetic subtrees

It has long been recognized that the rates of molecular evolution vary amongst sites in proteins. The usual model for rate heterogeneity assumes independent rate variation according to a rate distribution. In such models the rate at a site, although random, is assumed fixed throughout the evolutionary tree. Recent work by several groups has suggested that rates at sites often vary across subtrees of the larger tree as well as across sites. This phenomenon is not captured by most phylogenetic models but instead is more similar to the covarion model of Fitch and coworkers. In this article we present methods that can be useful in detecting whether different rates occur in two different subtrees of the larger tree and where these differences occur. Parametric bootstrapping and orthogonal regression methodologies are used to test for rate differences and to make statements about the general differences in the rates at sites. Confidence intervals based on the conditional distributions of rates at sites are then used to detect where the rate differences occur. Such methods will be helpful in studying the phylogenetic, structural, and functional bases of changes in evolutionary rates at sites, a phenomenon that has important consequences for deep phylogenetic inference.     

Covarion shifts cause a long-branch attraction artifact that unites microsporidia and archaebacteria in EF-1alpha phylogenies

Microsporidia branch at the base of eukaryotic phylogenies inferred from translation elongation factor 1alpha (EF-1alpha) sequences. Because these parasitic eukaryotes are fungi (or close relatives of fungi), it is widely accepted that fast-evolving microsporidian sequences are artifactually "attracted" to the long branch leading to the archaebacterial (outgroup) sequences ("long-branch attraction," or "LBA"). However, no previous studies have explicitly determined the reason(s) why the artifactual allegiance of microsporidia and archaebacteria ("M + A") is recovered by all phylogenetic methods, including maximum likelihood, a method that is supposed to be resistant to classical LBA. Here we show that the M + A affinity can be attributed to those alignment sites associated with large differences in evolutionary site rates between the eukaryotic and archaebacterial subtrees. Therefore, failure to model the significant evolutionary rate distribution differences (covarion shifts) between the ingroup and outgroup sequences is apparently responsible for the artifactual basal position of microsporidia in phylogenetic analyses of EF-1alpha sequences. Currently, no evolutionary model that accounts for discrete changes in the site rate distribution on particular branches is available for either protein or nucleotide level phylogenetic analysis, so the same artifacts may affect many other "deep" phylogenies. Furthermore, given the relative similarity of the site rate patterns of microsporidian and archaebacterial EF-1alpha proteins ("parallel site rate variation"), we suggest that the microsporidian orthologs may have lost some eukaryotic EF-1alpha-specific nontranslational functions, exemplifying the extreme degree of reduction in this parasitic lineage.     

Estimating and comparing the rates of gene discovery and expressed sequence tag (EST) frequencies in EST surveys

MOTIVATION: Expressed sequence tag (EST) surveys are an efficient way to characterize large numbers of genes from an organism. The rate of gene discovery in an EST survey depends on the degree of redundancy of the cDNA libraries from which sequences are obtained. However, few statistical methods have been developed to assess and compare redundancies of various libraries from preliminary EST surveys. RESULTS: We consider statistics for the comparison of EST libraries based upon the frequencies with which genes occur in subsamples of reads. These measures are useful in determining which one of several libraries is more likely to yield new genes in future reads and what proportion of additional reads one might want to take from the libraries in order to be likely to obtain new genes. One approach is to compare single sample measures that have been successfully used in species estimation problems, such as coverage of a library, defined as the proportion of the library that is represented in the given sample of reads. Another single library measure is an estimate of the expected number of additional genes that will be found in a new sample of reads. We also propose statistics that jointly use data from all the libraries. Analogous formulas for coverage and the expected numbers of new genes are presented. These measures consider coverage in a single library based upon reads from all libraries and similarly, the expected numbers of new genes that will be discovered by taking reads from all libraries with fixed proportions. Together, the statistics presented provide useful comparative measures for the libraries that can be used to guide sampling from each of the libraries to maximize the rate of gene discovery. Finally, we present tests for whether genes are equally represented or expressed in a set of libraries. Binomial and chi2 tests are presented for gene-by-gene comparisons of expression. Overall tests of the equality of proportional representation are presented and multiple comparisons issues are addressed. These methods can be used to evaluate changes in gene expression reflected in the composition of EST libraries prepared from different tissue types or cells exposed to different environmental conditions. AVAILABILITY: Software will be made available at http://www.mathstat.dal.ca/~tsusko     

Testing for covarion-like evolution in protein sequences

The covarion hypothesis of molecular evolution proposes that selective pressures on an amino acid or nucleotide site change through time, thus causing changes of evolutionary rate along the edges of a phylogenetic tree. Several kinds of Markov models for the covarion process have been proposed. One model, proposed by Huelsenbeck (2002), has 2 substitution rate classes: the substitution process at a site can switch between a single variable rate, drawn from a discrete gamma distribution, and a zero invariable rate. A second model, suggested by Galtier (2001), assumes rate switches among an arbitrary number of rate classes but switching to and from the invariable rate class is not allowed. The latter model allows for some sites that do not participate in the rate-switching process. Here we propose a general covarion model that combines features of both models, allowing evolutionary rates not only to switch between variable and invariable classes but also to switch among different rates when they are in a variable state. We have implemented all 3 covarion models in a maximum likelihood framework for amino acid sequences and tested them on 23 protein data sets. We found significant likelihood increases for all data sets for the 3 models, compared with a model that does not allow site-specific rate switches along the tree. Furthermore, we found that the general model fit the data better than the simpler covarion models in the majority of the cases, highlighting the complexity in modeling the covarion process. The general covarion model can be used for comparing tree topologies, molecular dating studies, and the investigation of protein adaptation.     

Phylogeny and Phytogeography of Eupatorium (Eupatorieae, Asteraceae): Insights from Sequence Data of the nrDNA ITS Regions and cpDNA RFLP

Eupatorium were examined by sequencing the internal transcribed spacers (ITS) of nuclear ribosomal DNA and restriction site analysis of chloroplast DNA. Molecular data provided strong evidence that (1) this genus originated in North America, (2) the genus diverged into three morphological species groups, Eutrochium, Traganthes and Uncasia in North America, and (3) one of the North American Uncasia lineages migrated into temperate Europe and eastern Asia over the Bering land bridge. The estimated divergence times support a late Miocene to early Pliocene migration from North America to Eurasia via the Bering land bridge. A European species was sister to all of the eastern Asian species examined. The disjunct distribution pattern of the genus Eupatorium is incongruent with the classical Arcto-Tertiary geoflora concept. Received 13 September 1999/ Accepted in revised form 4 January 2000