Evolutionarily distinctive species often capture more phylogenetic diversity than expected

Evolutionary distinctiveness measures of how evolutionarily isolated a species is relative to other members of its clade. Recently, distinctiveness metrics that explicitly incorporate time have been proposed for conservation prioritization. However, we found that such measures differ qualitatively in how well they capture the total amount of evolution (termed phylogenetic diversity, or PD) represented by a set of species. We used simulation and simple graph theory to explore this relationship with reference to phylogenetic tree shape. Overall, the distinctiveness measures capture more PD on more unbalanced trees and on trees with many splits near the present. The rank order of performance was robust across tree shapes, with apportioning measures performing best and node-based measures performing worst. A sample of 50 ultrametric trees from the literature showed the same patterns. Taken together, this suggests that distinctiveness metrics may be a useful addition to other measures of value for conservation prioritization of species. The simplest measure, the age of a species, performed surprisingly well, suggesting that new measures that focus on tree shape near the tips may provide a transparent alternative to more complicated full-tree approaches.     

Measures of stratigraphic fit to phylogeny and their sensitivity to tree size, tree shape, and scale

Measures of stratigraphic fit to phylogeny are analyzed to test how they are affected by the shape and size of the phylogenetic trees and by the number of stratigraphic intervals encompassed. Monte Carlo randomizations are used to investigate the sensitivity of three commonly used measures (SCI, GER and MSM*) approximating their distribution of possible values under certain conditions. All are shown to vary in different ways as parameters are varied, although MSM* seems to be the most invariant in the analyzed parameter space. These results suggest that the raw metrics should not be used for comparing the fit of different taxonomic groups or competing phylogenetic trees of the same group that differ in tree size or balance. Tree balance also affects the distributions used in significance tests based on randomization and therefore their results should not be interpreted in terms of the amount of conflict implied by a phylogenetic tree.     

All galls are divided into three or more parts: recursive enumeration of labeled histories for galled trees

Objective

In mathematical phylogenetics, a labeled rooted binary tree topology can possess any of a number of labeled histories, each of which represents a possible temporal ordering of its coalescences. Labeled histories appear frequently in calculations that describe the combinatorics of phylogenetic trees. Here, we generalize the concept of labeled histories from rooted phylogenetic trees to rooted phylogenetic networks, specifically for the class of rooted phylogenetic networks known as rooted galled trees.

Results

Extending a recursive algorithm for enumerating the labeled histories of a labeled tree topology, we present a method to enumerate the labeled histories associated with a labeled rooted galled tree. The method relies on a recursive decomposition by which each gall in a galled tree possesses three or more descendant subtrees. We exhaustively provide the numbers of labeled histories for all small galled trees, finding that each gall reduces the number of labeled histories relative to a specified galled tree that does not contain it.

Conclusion

The results expand the set of structures for which labeled histories can be enumerated, extending a well-known calculation for phylogenetic trees to a class of phylogenetic networks.

     

Mapping the Shapes of Phylogenetic Trees from Human and Zoonotic RNA Viruses

A phylogeny is a tree-based model of common ancestry that is an indispensable tool for studying biological variation. Phylogenies play a special role in the study of rapidly evolving populations such as viruses, where the proliferation of lineages is constantly being shaped by the mode of virus transmission, by adaptation to immune systems, and by patterns of human migration and contact. These processes may leave an imprint on the shapes of virus phylogenies that can be extracted for comparative study; however, tree shapes are intrinsically difficult to quantify. Here we present a comprehensive study of phylogenies reconstructed from 38 different RNA viruses from 12 taxonomic families that are associated with human pathologies. To accomplish this, we have developed a new procedure for studying phylogenetic tree shapes based on the ‘kernel trick’, a technique that maps complex objects into a statistically convenient space. We show that our kernel method outperforms nine different tree balance statistics at correctly classifying phylogenies that were simulated under different evolutionary scenarios. Using the kernel method, we observe patterns in the distribution of RNA virus phylogenies in this space that reflect modes of transmission and pathogenesis. For example, viruses that can establish persistent chronic infections (such as HIV and hepatitis C virus) form a distinct cluster. Although the visibly ‘star-like’ shape characteristic of trees from these viruses has been well-documented, we show that established methods for quantifying tree shape fail to distinguish these trees from those of other viruses. The kernel approach presented here potentially represents an important new tool for characterizing the evolution and epidemiology of RNA viruses.     

Phylogenetic Signal,Congruence, and Uncertainty across Bacteria and Archaea

Reconstruction of the Tree of Life is a central goal in biology. Although numerous novel phyla of bacteria and archaea have recently been discovered, inconsistent phylogenetic relationships are routinely reported, and many inter-phylum and inter-domain evolutionary relationships remain unclear. Here, we benchmark different marker genes often used in constructing multidomain phylogenetic trees of bacteria and archaea and present a set of marker genes that perform best for multidomain trees constructed from concatenated alignments. We use recently-developed Tree Certainty metrics to assess the confidence of our results and to obviate the complications of traditional bootstrap-based metrics. Given the vastly disparate number of genomes available for different phyla of bacteria and archaea, we also assessed the impact of taxon sampling on multidomain tree construction. Our results demonstrate that biases between the representation of different taxonomic groups can dramatically impact the topology of resulting trees. Inspection of our highest-quality tree supports the division of most bacteria into Terrabacteria and Gracilicutes, with Thermatogota and Synergistota branching earlier from these superphyla. This tree also supports the inclusion of the Patescibacteria within the Terrabacteria as a sister group to the Chloroflexota instead of as a basal-branching lineage. For the Archaea, our tree supports three monophyletic lineages (DPANN, Euryarchaeota, and TACK/Asgard), although we note the basal placement of the DPANN may still represent an artifact caused by biased sequence composition. Our findings provide a robust and standardized framework for multidomain phylogenetic reconstruction that can be used to evaluate inter-phylum relationships and assess uncertainty in conflicting topologies of the Tree of Life.     

Properties of phylogenetic trees generated by Yule-type speciation models

We investigate some discrete structural properties of evolutionary trees generated under simple null models of speciation, such as the Yule model. These models have been used as priors in Bayesian approaches to phylogenetic analysis, and also to test hypotheses concerning the speciation process. In this paper we describe new results for three properties of trees generated under such models. Firstly, for a rooted tree generated by the Yule model we describe the probability distribution on the depth (number of edges from the root) of the most recent common ancestor of a random subset of k species. Next we show that, for trees generated under the Yule model, the approximate position of the root can be estimated from the associated unrooted tree, even for trees with a large number of leaves. Finally, we analyse a biologically motivated extension of the Yule model and describe its distribution on tree shapes when speciation occurs in rapid bursts.     

CENTRAL MOMENTS AND PROBABILITY DISTRIBUTION OF COLLESS'S COEFFICIENT OF TREE IMBALANCE

The great increase in the number of phylogenetic studies of a wide variety of organisms in recent decades has focused considerable attention on the balance of phylogenetic trees—the degree to which sister clades within a tree tend to be of equal size—for at least two reasons: (1) the degree of balance of a tree may affect the accuracy of estimates of it; (2) the degree of balance, or imbalance, of a tree may reveal something about the macroevolutionary processes that produced it. In particular, variation among lineages in rates of speciation or extinction is expected to produce trees that are less balanced than those that result from phylogenetic evolution in which each extant species of a group has the same probability of speciation or extinction. Several coefficients for measuring the balance or imbalance of phylogenetic trees have been proposed. I focused on Colless's coefficient of imbalance (7) for its mathematical tractability and ease of interpretation. Earlier work on this statistic produced exact methods only for calculating the expected value. In those studies, the variance and confidence limits, which are necessary for testing the departure of observed values of I from the expected, were estimated by Monte Carlo simulation. I developed recursion equations that allow exact calculation of the mean, variance, skewness, and complete probability distribution of I for two different probability-generating models for bifurcating tree shapes. The Equal-Rates Markov (ERM) model assumes that trees grow by the random speciation and extinction of extant species, with all species that are extant at a given time having the same probability of speciation or extinction. The Equal Probability (EP) model assumes that all possible labeled trees for a given number of terminal taxa have the same probability of occurring. Examples illustrate how these theoretically derived probabilities and parameters may be used to test whether the evolution of a monophyletic group or set of monophyletic groups has proceeded according to a Markov model with equal rates of speciation and extinction among species, that is, whether there has been significant variation among lineages in expected rates of speciation or extinction.     

A heuristic approach of maximum likelihood method for inferring phylogenetic tree and an application to the mammalian SOX-3 origin of the testis-determining gene SRY

Applying the tree bisection and reconnection (TBR) algorithm, we have developed a heuristic method (maximum likelihood (ML)-TBR) for inferring the ML tree based on tree topology search. For initial trees from which iterative processes start in ML-TBR, two cases were considered: one is 100 neighbor-joining (NJ) trees based on the bootstrap resampling and the other is 100 randomly generated trees. The same ML tree was obtained in both cases. All different iterative processes started from 100 independent initial trees ultimately converged on one optimum tree with the largest log-likelihood value, suggesting that a limited number of initial trees will be quite enough in ML-TBR. This also suggests that the optimum tree corresponds to the global optimum in tree topology space and thus probably coincides with the ML tree inferred by intact ML analysis. This method has been applied to the inference of phylogenetic tree of the SOX family members. The mammalian testis-determining gene SRY is believed to have evolved from SOX-3, a member of the SOX family, based on several lines of evidence, including their sequence similarity, the location of SOX-3 on the X chromosome and some aspects of their expression. This model should be supported directly from the phylogenetic tree of the SOX family, but no evidence has been provided to date. A recently published NJ tree shows implausibly remote origin of SRY, suggesting that a more sophisticated method is required for understanding this problem. The ML tree inferred by the present method showed that the SRYs of marsupial and placental mammals form a monophyletic cluster which had diverged from the mammalian SOX-3 in the early evolution of mammals.     

TreeSnatcher: coding trees from images

TreeSnatcher is a GUI-driven JAVA application for the semi-automatic recognition of multifurcating phylogenetic trees in pixel images. The program accepts an image file as input and analyzes the topology and the metrics of a tree depicted. The analysis is carried out in a multiple-stage process using algorithms from image analysis. In the end, TreeSnatcher produces a Newick tree code that represents the tree structure optionally including branch lengths. TreeSnatcher can process trees with 100 leaves or more in a few seconds. AVAILABILITY: TreeSnatcher was developed in JAVA under Mac OS X and is executable on UNIX/Linux, Windows and Mac OS X systems. The application and its documentation can be freely downloaded from http://www.cibiv.at/software/treesnatcher.     

Unicyclic networks: compatibility and enumeration

Graphs obtained from a binary leaf labeled ("phylogenetic") tree by adding an edge so as to introduce a cycle provide a useful representation of hybrid evolution in molecular evolutionary biology. This class of graphs (which we call "unicyclic networks") also has some attractive combinatorial properties, which we present. We characterize when a set of binary phylogenetic trees is displayed by a unicyclic network in terms of tree rearrangement operations. This leads to a triple-wise compatibility theorem and a simple, fast algorithm to determine 1-cycle compatibility. We also use generating function techniques to provide closed-form expressions that enumerate unicyclic networks with specified or unspecified cycle length, and we provide an extension to enumerate a class of multicyclic networks.     

treespace: Statistical exploration of landscapes of phylogenetic trees

The increasing availability of large genomic data sets as well as the advent of Bayesian phylogenetics facilitates the investigation of phylogenetic incongruence, which can result in the impossibility of representing phylogenetic relationships using a single tree. While sometimes considered as a nuisance, phylogenetic incongruence can also reflect meaningful biological processes as well as relevant statistical uncertainty, both of which can yield valuable insights in evolutionary studies. We introduce a new tool for investigating phylogenetic incongruence through the exploration of phylogenetic tree landscapes. Our approach, implemented in the R package treespace , combines tree metrics and multivariate analysis to provide low‐dimensional representations of the topological variability in a set of trees, which can be used for identifying clusters of similar trees and group‐specific consensus phylogenies. treespace also provides a user‐friendly web interface for interactive data analysis and is integrated alongside existing standards for phylogenetics. It fills a gap in the current phylogenetics toolbox in R and will facilitate the investigation of phylogenetic results.     

Analysis and visualization of tree space

We explored the use of multidimensional scaling (MDS) of tree-to-tree pairwise distances to visualize the relationships among sets of phylogenetic trees. We found the technique to be useful for exploring "tree islands" (sets of topologically related trees among larger sets of near-optimal trees), for comparing sets of trees obtained from bootstrapping and Bayesian sampling, for comparing trees obtained from the analysis of several different genes, and for comparing multiple Bayesian analyses. The technique was also useful as a teaching aid for illustrating the progress of a Bayesian analysis and as an exploratory tool for examining large sets of phylogenetic trees. We also identified some limitations to the method, including distortions of the multidimensional tree space into two dimensions through the MDS technique, and the definition of the MDS-defined space based on a limited sample of trees. Nonetheless, the technique is a useful approach for the analysis of large sets of phylogenetic trees.     

Metrics for Phylogenetic Networks II: Nodal and Triplets Metrics

The assessment of phylogenetic network reconstruction methods requires the ability to compare phylogenetic networks. This is the second in a series of papers devoted to the analysis and comparison of metrics for tree-child time consistent phylogenetic networks on the same set of taxa. In this paper, we generalize to phylogenetic networks two metrics that have already been introduced in the literature for phylogenetic trees: the nodal distance and the triplets distance. We prove that they are metrics on any class of tree-child time consistent phylogenetic networks on the same set of taxa, as well as some basic properties for them. To prove these results, we introduce a reduction/expansion procedure that can be used not only to establish properties of tree-child time consistent phylogenetic networks by induction, but also to generate all tree-child time consistent phylogenetic networks with a given number of leaves.     

Estimation of phylogenetic inconsistencies in the three domains of life

Discrepancies in phylogenetic trees of bacteria and archaea are often explained as lateral gene transfer events. However, such discrepancies may also be due to phylogenetic artifacts or orthology assignment problems. A first step that may help to resolve this dilemma is to estimate the extent of phylogenetic inconsistencies in trees of prokaryotes in comparison with those of higher eukaryotes, where no lateral gene transfer is expected. To test this, we used 21 proteomes each of eukaryotes (mainly opisthokonts), proteobacteria, and archaea that spanned equivalent levels of genetic divergence. In each domain of life, we defined a set of putative orthologous sequences using a phylogenetic-based orthology protocol and, as a reference topology, we used a tree constructed with concatenated genes of each domain. Our results show, for most of the tests performed, that the magnitude of topological inconsistencies with respect to the reference tree was very similar in the trees of proteobacteria and eukaryotes. When clade support was taken into account, prokaryotes showed some more inconsistencies, but then all values were very low. Discrepancies were only consistently higher in archaea but, as shown by simulation analysis, this is likely due to the particular tree of the archaeal species used here being more difficult to reconstruct, whereas the trees of proteobacteria and eukaryotes were of similar difficulty. Although these results are based on a relatively small number of genes, it seems that phylogenetic reconstruction problems, including orthology assignment problems, have a similar overall effect over prokaryotic and eukaryotic trees based on single genes. Consequently, lateral gene transfer between distant prokaryotic species may have been more rare than previously thought, which opens the way to obtain the tree of life of bacterial and archaeal species using genomic data and the concatenation of adequate genes, in the same way as it is usually done in eukaryotes.     

Effect of site-specific heterogeneous evolution on phylogenetic reconstruction: a simple evaluation

Recent studies have shown that heterogeneous evolution may mislead phylogenetic analysis, which has been neglected for a long time. We evaluate the effect of heterogeneous evolution on phylogenetic analysis, using 18 fish mitogenomic coding sequences as an example. Using the software DIVERGE, we identify 198 amino acid sites that have experienced heterogeneous evolution. After removing these sites, the rest of sites are shown to be virtually homogeneous in the evolutionary rate. There are some differences between phylogenetic trees built with heterogeneous sites ("before tree") and without heterogeneous sites ("after tree"). Our study demonstrates that for phylogenetic reconstruction, an effective approach is to identify and remove sites with heterogeneous evolution, and suggests that researchers can use the software DIVERGE to remove the influence of heterogeneous evolution before reconstructing phylogenetic trees.     

Characterization of reticulate networks based on the coalescent with recombination

Phylogenetic networks aim to represent the evolutionary history of taxa. Within these, reticulate networks are explicitly able to accommodate evolutionary events like recombination, hybridization, or lateral gene transfer. Although several metrics exist to compare phylogenetic networks, they make several assumptions regarding the nature of the networks that are not likely to be fulfilled by the evolutionary process. In order to characterize the potential disagreement between the algorithms and the biology, we have used the coalescent with recombination to build the type of networks produced by reticulate evolution and classified them as regular, tree sibling, tree child, or galled trees. We show that, as expected, the complexity of these reticulate networks is a function of the population recombination rate. At small recombination rates, most of the networks produced are already more complex than regular or tree sibling networks, whereas with moderate and large recombination rates, no network fit into any of the standard classes. We conclude that new metrics still need to be devised in order to properly compare two phylogenetic networks that have arisen from reticulating evolutionary process.     

Improvement of phylogenies after removing divergent and ambiguously aligned blocks from protein sequence alignments

Alignment quality may have as much impact on phylogenetic reconstruction as the phylogenetic methods used. Not only the alignment algorithm, but also the method used to deal with the most problematic alignment regions, may have a critical effect on the final tree. Although some authors remove such problematic regions, either manually or using automatic methods, in order to improve phylogenetic performance, others prefer to keep such regions to avoid losing any information. Our aim in the present work was to examine whether phylogenetic reconstruction improves after alignment cleaning or not. Using simulated protein alignments with gaps, we tested the relative performance in diverse phylogenetic analyses of the whole alignments versus the alignments with problematic regions removed with our previously developed Gblocks program. We also tested the performance of more or less stringent conditions in the selection of blocks. Alignments constructed with different alignment methods (ClustalW, Mafft, and Probcons) were used to estimate phylogenetic trees by maximum likelihood, neighbor joining, and parsimony. We show that, in most alignment conditions, and for alignments that are not too short, removal of blocks leads to better trees. That is, despite losing some information, there is an increase in the actual phylogenetic signal. Overall, the best trees are obtained by maximum-likelihood reconstruction of alignments cleaned by Gblocks. In general, a relaxed selection of blocks is better for short alignment, whereas a stringent selection is more adequate for longer ones. Finally, we show that cleaned alignments produce better topologies although, paradoxically, with lower bootstrap. This indicates that divergent and problematic alignment regions may lead, when present, to apparently better supported although, in fact, more biased topologies.     

A genetic algorithm for maximum-likelihood phylogeny inference using nucleotide sequence data

Phylogeny reconstruction is a difficult computational problem, because the number of possible solutions increases with the number of included taxa. For example, for only 14 taxa, there are more than seven trillion possible unrooted phylogenetic trees. For this reason, phylogenetic inference methods commonly use clustering algorithms (e.g., the neighbor-joining method) or heuristic search strategies to minimize the amount of time spent evaluating nonoptimal trees. Even heuristic searches can be painfully slow, especially when computationally intensive optimality criteria such as maximum likelihood are used. I describe here a different approach to heuristic searching (using a genetic algorithm) that can tremendously reduce the time required for maximum-likelihood phylogenetic inference, especially for data sets involving large numbers of taxa. Genetic algorithms are simulations of natural selection in which individuals are encoded solutions to the problem of interest. Here, labeled phylogenetic trees are the individuals, and differential reproduction is effected by allowing the number of offspring produced by each individual to be proportional to that individual's rank likelihood score. Natural selection increases the average likelihood in the evolving population of phylogenetic trees, and the genetic algorithm is allowed to proceed until the likelihood of the best individual ceases to improve over time. An example is presented involving rbcL sequence data for 55 taxa of green plants. The genetic algorithm described here required only 6% of the computational effort required by a conventional heuristic search using tree bisection/reconnection (TBR) branch swapping to obtain the same maximum-likelihood topology.      

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.