Five statistical questions about the tree of life

Stochastic modeling of phylogenies raises five questions that have received varying levels of attention from quantitatively inclined biologists. 1) How large do we expect (from the model) the ratio of maximum historical diversity to current diversity to be? 2) From a correct phylogeny of the extant species of a clade, what can we deduce about past speciation and extinction rates? 3) What proportion of extant species are in fact descendants of still-extant ancestral species, and how does this compare with predictions of models? 4) When one moves from trees on species to trees on sets of species (whether traditional higher order taxa or clades within PhyloCode), does one expect trees to become more unbalanced as a purely logical consequence of tree structure, without signifying any real biological phenomenon? 5) How do we expect that fluctuation rates for counts of higher order taxa should compare with fluctuation rates for number of species? We present a mathematician's view based on an oversimplified modeling framework in which all these questions can be studied coherently.     

Nodes in phylogenetic trees: the relation between imbalance and number of descendent species

The imbalance of a node in a phylogenetic tree can be defined in terms of the relative numbers of species (or higher taxa) on the branches that originate at the node. Empirically, imbalance also turns out to depend on the absolute total number of species on the branches: in a sample of large trees, nodes with more descendent species tend to be more unbalanced. Subsidiary analyses suggest that this pattern is not a result of errors in tree estimation. Instead, the increase in imbalance with species is consistent with a cumulative effect of differences in diversification rates between branches. [Equal-rates Markov model; imbalance; phylogeny shape; proportional-to-distinguishable-arrangements model.].     

ADAPTIVE RADIATION AND THE TOPOLOGY OF LARGE PHYLOGENIES

The idea that some organisms possess adaptive features that make them more likely to speciate and/or less likely to go extinct than closely related groups, suggests that large phylogenetic trees should be unbalanced (more species should occur in the group possessing the adaptive features than in the sister group lacking such features). Several methods have been used to document this type of adaptive radiation. One problem with these attempts is that evolutionary biologists may overlook balanced phylogenies while focusing on a few impressively unbalanced ones. To overcome this potential bias, we sampled published large phylogenies without regard to tree shape. These were used to test whether or not such trees are consistently unbalanced. We used recently developed null models to demonstrate that the shapes of large phylogenetic trees: 1) are similar among angiosperms, insects, and tetrapods; 2) differ from those expected due to random selection of a phylogeny from the pool of all trees of similar size; and 3) are significantly more unbalanced than expected if species diverge at random, therefore, conforming to one prediction of adaptive radiation. This represents an important first step in documenting whether adaptive radiation has been a general feature of evolution.     

Trees of trees: an approach to comparing multiple alternative phylogenies

Phylogenetic analysis very commonly produces several alternative trees for a given fixed set of taxa. For example, different sets of orthologous genes may be analyzed, or the analysis may sample from a distribution of probable trees. This article describes an approach to comparing and visualizing multiple alternative phylogenies via the idea of a "tree of trees" or "meta-tree." A meta-tree clusters phylogenies with similar topologies together in the same way that a phylogeny clusters species with similar DNA sequences. Leaf nodes on a meta-tree correspond to the original set of phylogenies given by some analysis, whereas interior nodes correspond to certain consensus topologies. The construction of meta-trees is motivated by analogy with construction of a most parsimonious tree for DNA data, but instead of using DNA letters, in a meta-tree the characters are partitions or splits of the set of taxa. An efficient algorithm for meta-tree construction is described that makes use of a known relationship between the majority consensus and parsimony in terms of gain and loss of splits. To illustrate these ideas meta-trees are constructed for two datasets: a set of gene trees for species of yeast and trees from a bootstrap analysis of a set of gene trees in ray-finned fish. A software tool for constructing meta-trees and comparing alternative phylogenies is available online, and the source code can be obtained from the author.     

A quantitative assessment of congruence between molecular and nonmolecular estimates of phylogeny

Summary An important means of assessing the validity of phylogenetic hypotheses is to measure congruence between different studies of the same group. We applied statistical methods to assess patterns of congruence among phylogenies taken from the literature, using strict-consensus and quartet statistics to measure congruence for 48 pairs of phylogenies of various groups of birds and mammals. The strict-consensus measures were higher on average for distance-distance comparisons than for distance-parsimony or parsimony-parsimony comparisons, and for molecular-molecular comparisons than for molecular-morphological or morphological-morphological comparisons. However, the only factor that was consistently important statistically was the number of taxa involved in the comparison, with congruence decreasing as the number of taxa increased. Quartet indices, which measure network similarity regardless of root position, also showed an effect based on number of taxa but exhibited no trend toward higher congruence in molecular-molecular and distance-distance comparisons. The number of studies with jointly unresolved quartets was small, indicating that data sets varied in the degree to which they could resolve relationships at different phylogenetic levels.The levels of congruence between phylogenies, including those employing single-copy nuclear DNA hybridization data, appear to be higher than expected in random sets of trees, cannot be explained by nonindependence of data sets, and thus provide empirical support for the validity of both distance and parsimony methods of phylogenetic inference. In specific instances, low congruence pointed to mistakes in the application of certain methods, and to the existence of problem taxa in need of additional study.     

Improved parameterized complexity of the maximum agreement subtree and maximum compatible tree problems

Given a set of evolutionary trees on a same set of taxa, the maximum agreement subtree problem (MAST), respectively, maximum compatible tree problem (MCT), consists of finding a largest subset of taxa such that all input trees restricted to these taxa are isomorphic, respectively compatible. These problems have several applications in phylogenetics such as the computation of a consensus of phylogenies obtained from different data sets, the identification of species subjected to horizontal gene transfers and, more recently, the inference of supertrees, e.g., Trees Of Life. We provide two linear time algorithms to check the isomorphism, respectively, compatibility, of a set of trees or otherwise identify a conflict between the trees with respect to the relative location of a small subset of taxa. Then, we use these algorithms as subroutines to solve MAST and MCT on rooted or unrooted trees of unbounded degree. More precisely, we give exact fixed-parameter tractable algorithms, whose running time is uniformly polynomial when the number of taxa on which the trees disagree is bounded. The improves on a known result for MAST and proves fixed-parameter tractability for MCT.     

DOES IMBALANCE IN PHYLOGENIES REFLECT ONLY BIAS?

Phylogenetic tree imbalance was originally believed to indicate differences in evolutionary rates within trees, but other sources of imbalance have been identified, such as tree incompleteness and low quality of the data. To examine the effect of data quality, I calculated Colless's index for 69 recent complete phylogenies. On average, these phylogenies were more unbalanced than phylogenies generated by the equal rates Markov (ERM) model. I tried Mooers's (1995) method to correct for tree size, but his measure appeared to become dependent on tree size when there are large trees (i.e., > 14 tips) in a collection. Instead I corrected for tree size by taking the difference between Colless's index of observed trees and the ERM model expectation for a tree of the same size. The balance measure thus obtained did not correlate significantly to consistency and retention indices as indicators of data quality. It was also independent of the factors kingdom (plants and animals) and taxon level at the tips and type of data (molecular, morphological, and combined).     

Comparing tree shapes: beyond symmetry

This paper describes two types of problems related to tree shapes, as well as algorithms that can be used to solve these problems. The first problem is that of comparing the similarity of the unlabelled shapes instead of merely their degree of balance, in a manner analogous to that routinely used to compare topologies for labelled trees. There are possible practical applications for this comparison, such as determining, based on tree shape similarity alone, whether the taxa in two phylogenies are likely to have a correspondence (e.g. hosts and parasites with high specificity). It is shown that tree balance is insufficient for this task and that standard measures of topological difference (Robinson–Foulds distances, SPR distances or retention indices of the matrices representing the trees, MRPs) can be easily adapted to the problem. The second type of problem is to determine whether taxa of uncertain matching unique to two different phylogenies could correspond to each other (e.g. the same species in larvae and adults of metamorphic animals, fossils known from different body parts). This second problem can be solved by either relabelling taxa in such a way that the number of consensus nodes is maximized, or relabelling taxa in such a way that the sum of the number of steps in the MRP of each tree mapped onto the other is minimum.     

Assessing the performance of single-copy genes for recovering robust phylogenies

Phylogenies involving nonmodel species are based on a few genes, mostly chosen following historical or practical criteria. Because gene trees are sometimes incongruent with species trees, the resulting phylogenies may not accurately reflect the evolutionary relationships among species. The increase in availability of genome sequences now provides large numbers of genes that could be used for building phylogenies. However, for practical reasons only a few genes can be sequenced for a wide range of species. Here we asked whether we can identify a few genes, among the single-copy genes common to most fungal genomes, that are sufficient for recovering accurate and well-supported phylogenies. Fungi represent a model group for phylogenomics because many complete fungal genomes are available. An automated procedure was developed to extract single-copy orthologous genes from complete fungal genomes using a Markov Clustering Algorithm (Tribe-MCL). Using 21 complete, publicly available fungal genomes with reliable protein predictions, 246 single-copy orthologous gene clusters were identified. We inferred the maximum likelihood trees using the individual orthologous sequences and constructed a reference tree from concatenated protein alignments. The topologies of the individual gene trees were compared to that of the reference tree using three different methods. The performance of individual genes in recovering the reference tree was highly variable. Gene size and the number of variable sites were highly correlated and significantly affected the performance of the genes, but the average substitution rate did not. Two genes recovered exactly the same topology as the reference tree, and when concatenated provided high bootstrap values. The genes typically used for fungal phylogenies did not perform well, which suggests that current fungal phylogenies based on these genes may not accurately reflect the evolutionary relationships among species. Analyses on subsets of species showed that the phylogenetic performance did not seem to depend strongly on the sample. We expect that the best-performing genes identified here will be very useful for phylogenetic studies of fungi, at least at a large taxonomic scale. Furthermore, we compare the method developed here for finding genes for building robust phylogenies with previous ones and we advocate that our method could be applied to other groups of organisms when more complete genomes are available.     

Which molecular markers for assessing which taxonomic level? The case study of the mite family Phytoseiidae (Acari: Mesostigmata)

The use of molecular markers for resolving systematics issues has improved our knowledge of life history. However, for the taxa studied herein—the predatory mite family Phytoseiidae—molecular phylogeny is impeded by a lack of suitable markers for deeper taxonomic levels. This study aims (i) to establish DNA amplification protocols for molecular markers known to resolve supraspecific nodes in other taxa, (ii) to determine their individual performance in assessing the clustering of species, genera, tribes and subfamilies, and (iii) to characterize the additional information provided when markers are concatenated. A new phylogenetic index is proposed based on ecological concepts, considering trees as a community of nodes. New and efficient protocols for DNA amplification of six molecular markers are provided. The concatenated tree globally provides more robust and reliable information, especially for deeper nodes. However, for assessing species identification and within‐genera phylogenies, the combined use of six markers does not seem necessary, underlining the need to resize experiments depending on their taxonomic objectives. Finally, this study lays the methodological foundations with which to test the present Phytoseiidae classification as the first phylogeny obtained shows incongruence with the present morphological classification.     

When can host shifts produce congruent host and parasite phylogenies? A simulation approach

Congruence between host and parasite phylogenies is often taken as evidence for cospeciation. However, 'pseudocospeciation', resulting from host-switches followed by parasite speciation, may also generate congruent trees. To investigate this process and the conditions favouring its appearance, we here simulated the adaptive radiation of a parasite onto a new range of hosts. A very high congruence between the host tree and the resulting parasite trees was obtained when parasites switched between closely related hosts. Setting a shorter time lag for speciation after switches between distantly related hosts further increased the degree of congruence. The shape of the host tree, however, had a strong impact, as no congruence could be obtained when starting with highly unbalanced host trees. The strong congruences obtained were erroneously interpreted as the result of cospeciations by commonly used phylogenetic software packages despite the fact that all speciations resulted from host-switches in our model. These results highlight the importance of estimating the age of nodes in host and parasite phylogenies when testing for cospeciation and also demonstrate that the results obtained with software packages simulating evolutionary events must be interpreted with caution.     

Likelihood Inference of Non-Constant Diversification Rates with Incomplete Taxon Sampling

Large-scale phylogenies provide a valuable source to study background diversification rates and investigate if the rates have changed over time. Unfortunately most large-scale, dated phylogenies are sparsely sampled (fewer than 5% of the described species) and taxon sampling is not uniform. Instead, taxa are frequently sampled to obtain at least one representative per subgroup (e.g. family) and thus to maximize diversity (diversified sampling). So far, such complications have been ignored, potentially biasing the conclusions that have been reached. In this study I derive the likelihood of a birth-death process with non-constant (time-dependent) diversification rates and diversified taxon sampling. Using simulations I test if the true parameters and the sampling method can be recovered when the trees are small or medium sized (fewer than 200 taxa). The results show that the diversification rates can be inferred and the estimates are unbiased for large trees but are biased for small trees (fewer than 50 taxa). Furthermore, model selection by means of Akaike''s Information Criterion favors the true model if the true rates differ sufficiently from alternative models (e.g. the birth-death model is recovered if the extinction rate is large and compared to a pure-birth model). Finally, I applied six different diversification rate models – ranging from a constant-rate pure birth process to a decreasing speciation rate birth-death process but excluding any rate shift models – on three large-scale empirical phylogenies (ants, mammals and snakes with respectively 149, 164 and 41 sampled species). All three phylogenies were constructed by diversified taxon sampling, as stated by the authors. However only the snake phylogeny supported diversified taxon sampling. Moreover, a parametric bootstrap test revealed that none of the tested models provided a good fit to the observed data. The model assumptions, such as homogeneous rates across species or no rate shifts, appear to be violated.     

Molecular phylogeny of selected Old World Astragalus (Fabaceae): incongruence among chloroplast trnL-F, ndhF and nuclear ribosomal DNA ITS sequences

This study reports maximum parsimony and Bayesian phylogenetic analyses of selected Old World Astragalus using two chloroplast fragments including trnL-F and ndhF and the nuclear ribosomal internal transcribed spacer (nrDNA ITS). A total of 52 taxa including 34 euploid Old World and New World Astragalus , one aneuploid species from the Neo-Astragalus clade as a representative and 14 other Astragalean taxa, plus Cheseneya astragalina and two species of Caragana as outgroups were analyzed for both trnL-F and nrDNA ITS regions. ndhF was analyzed in 30 taxa and the same number for the combination of these three datasets were examined. In general, the trnL-F dataset and the ndhF and nrDNA ITS datasets generated more or less the same clades within Astragalus . However, in the trnL-F and ndhF phylogenies, Astragalus species are not gathered in a single clade, the so-called Astragalus s.s., as indicated by the nrDNA ITS tree. Visual inspection of these three phylogenies revealed that they were inconsistent regarding the position and relationships of Astragalus hemsleyi , A. ophiocarpus , A. annularis–A. epiglottis / Astragalus pelecinus, A. echinatus and A. arizonicus . Incongruence length difference test suggested that the trnL-F , ndhF and nrDNA ITS datasets were incongruent. In spite of this, phylogenetic analyses of the combined datasets as one unit or as three partitions generated trees that were topologically similar as a mix of the cpDNA and the nrDNA ITS trees. However, the combined dataset provided more resolved and statistically supported clades. The recently described A. memoriosus appeared closely related to A. stocksii (both from sect. Caraganella ) based on both trnL-F and nrDNA ITS sequences.     

Exploring the relationship between sequence similarity and accurate phylogenetic trees

We have characterized the relationship between accurate phylogenetic reconstruction and sequence similarity, testing whether high levels of sequence similarity can consistently produce accurate evolutionary trees. We generated protein families with known phylogenies using a modified version of the PAML/EVOLVER program that produces insertions and deletions as well as substitutions. Protein families were evolved over a range of 100-400 point accepted mutations; at these distances 63% of the families shared significant sequence similarity. Protein families were evolved using balanced and unbalanced trees, with ancient or recent radiations. In families sharing statistically significant similarity, about 60% of multiple sequence alignments were 95% identical to true alignments. To compare recovered topologies with true topologies, we used a score that reflects the fraction of clades that were correctly clustered. As expected, the accuracy of the phylogenies was greatest in the least divergent families. About 88% of phylogenies clustered over 80% of clades in families that shared significant sequence similarity, using Bayesian, parsimony, distance, and maximum likelihood methods. However, for protein families with short ancient branches (ancient radiation), only 30% of the most divergent (but statistically significant) families produced accurate phylogenies, and only about 70% of the second most highly conserved families, with median expectation values better than 10(-60), produced accurate trees. These values represent upper bounds on expected tree accuracy for sequences with a simple divergence history; proteins from 700 Giardia families, with a similar range of sequence similarities but considerably more gaps, produced much less accurate trees. For our simulated insertions and deletions, correct multiple sequence alignments did not perform much better than those produced by T-COFFEE, and including sequences with expressed sequence tag-like sequencing errors did not significantly decrease phylogenetic accuracy. In general, although less-divergent sequence families produce more accurate trees, the likelihood of estimating an accurate tree is most dependent on whether radiation in the family was ancient or recent. Accuracy can be improved by combining genes from the same organism when creating species trees or by selecting protein families with the best bootstrap values in comprehensive studies.     

Phylogenetic congruence of mealybugs and their primary endosymbionts

Tight interactions between unrelated organisms such as is seen in plant-insect, host-parasite, or host-symbiont associations may lead to speciation of the smaller partners when their hosts speciate. Totally congruent phylogenies of interacting taxa have not been observed often but a number of studies have provided evidence that various hemipteran insect taxa and their primary bacterial endosymbionts share phylogenetic histories. Like other hemipterans, mealybugs (Pseudococcidae) harbour multiple intracellular bacterial symbionts, which are thought to be strictly vertically inherited, implying codivergence of hosts and symbionts. Here, robust estimates of phylogeny were generated from four fragments of three nuclear genes for mealybugs of the subfamily Pseudococcinae, and a substantial fragment of the 16S-23S rDNA of their P-endosymbionts. Phylogenetic congruence was highly significant, with 75% of nodes on the two trees identical, and significant correlation of branch lengths indicated coincident timing of cladogenesis. It is suggested that the low level of observed incongruence was influenced by uncertainty in phylogenetic estimation, but evolutionary outcomes other than congruence, including host shifts, could not be rejected.     

A data based parsimony method of cophylogenetic analysis

Phylogenies of closely interacting groups, such as hosts and parasites, are seldom completely congruent. Incongruence can arise from biologically meaningful differences in the histories of the two groups, or can be generated by artifactual differences that are merely the result of incorrect phylogenies with weakly supported nodes. We present a method that distinguishes between these sources of incongruence and identifies lineages that are responsible for significant differences between phylogenies. We use the logic of conditional combination in that we first test for statistically significant incongruence using the partition homogeneity test. Then we remove all possible combinations of taxa until a non-significant result of this test is achieved. Finally, we construct a 'combined evidence' phylogeny and then reposition the incongruent taxa. This method produces trees for final comparison using reconciliation methods, but it includes only as many incongruence events as can be statistically justified from the data sets. We apply this method to a host–parasite (gopher–louse) data set and identify many fewer incongruence events than do topology based analyses alone. Our method is broadly applicable to comparisons of phylogenies of interacting taxa, such as hosts and parasites, or mutualists. The method should also be useful for other problems involving comparisons of phylogenies, such as multiple gene trees or cladistic biogeography.     

More taxa or more characters revisited: combining data from nuclear protein-encoding genes for phylogenetic analyses of Noctuoidea (Insecta: Lepidoptera)

A central question concerning data collection strategy for molecular phylogenies has been, is it better to increase the number of characters or the number of taxa sampled to improve the robustness of a phylogeny estimate? A recent simulation study concluded that increasing the number of taxa sampled is preferable to increasing the number of nucleotide characters, if taxa are chosen specifically to break up long branches. We explore this hypothesis by using empirical data from noctuoid moths, one of the largest superfamilies of insects. Separate studies of two nuclear genes, elongation factor-1 alpha (EF-1 alpha) and dopa decarboxylase (DDC), have yielded similar gene trees and high concordance with morphological groupings for 49 exemplar species. However, support levels were quite low for nodes deeper than the subfamily level. We tested the effects on phylogenetic signal of (1) increasing the taxon sampling by nearly 60%, to 77 species, and (2) combining data from the two genes in a single analysis. Surprisingly, the increased taxon sampling, although designed to break up long branches, generated greater disagreement between the two gene data sets and decreased support levels for deeper nodes. We appear to have inadvertently introduced new long branches, and breaking these up may require a yet larger taxon sample. Sampling additional characters (combining data) greatly increased the phylogenetic signal. To contrast the potential effect of combining data from independent genes with collection of the same total number of characters from a single gene, we simulated the latter by bootstrap augmentation of the single-gene data sets. Support levels for combined data were at least as high as those for the bootstrap-augmented data set for DDC and were much higher than those for the augmented EF-1 alpha data set. This supports the view that in obtaining additional sequence data to solve a refractory systematic problem, it is prudent to take them from an independent gene.     

Divergence time estimation using fossils as terminal taxa and the origins of Lissamphibia

Were molecular data available for extinct taxa, questions regarding the origins of many groups could be settled in short order. As this is not the case, various strategies have been proposed to combine paleontological and neontological data sets. The use of fossil dates as node age calibrations for divergence time estimation from molecular phylogenies is commonplace. In addition, simulations suggest that the addition of morphological data from extinct taxa may improve phylogenetic estimation when combined with molecular data for extant species, and some studies have merged morphological and molecular data to estimate combined evidence phylogenies containing both extinct and extant taxa. However, few, if any, studies have attempted to estimate divergence times using phylogenies containing both fossil and living taxa sampled for both molecular and morphological data. Here, I infer both the phylogeny and the time of origin for Lissamphibia and a number of stem tetrapods using Bayesian methods based on a data set containing morphological data for extinct taxa, molecular data for extant taxa, and molecular and morphological data for a subset of extant taxa. The results suggest that Lissamphibia is monophyletic, nested within Lepospondyli, and originated in the late Carboniferous at the earliest. This research illustrates potential pitfalls for the use of fossils as post hoc age constraints on internal nodes and highlights the importance of explicit phylogenetic analysis of extinct taxa. These results suggest that the application of fossils as minima or maxima on molecular phylogenies should be supplemented or supplanted by combined evidence analyses whenever possible.     

Cospeciation between bacterial endosymbionts (Buchnera) and a recent radiation of aphids (Uroleucon) and pitfalls of testing for phylogenetic congruence

Abstract.— Previous studies of phylogenetic congruence between aphids and their symbiotic bacteria ( Buchnera ) supported long-term vertical transmission of symbionts. However, those studies were based on distantly related aphids and would not have revealed horizontal transfer of symbionts among closely related hosts. Aphid species of the genus Uroleucon are closely related phylogenetically and overlap in geographic ranges, habitats, and parasitoids. To examine support for congruence of phylogenies of Buchnera and Uroleucon , sequences from four mitochondrial, one nuclear, and one endosymbiont gene ( trpB ) were obtained. Congruence of phylogenies based on pooled aphid genes with phylogenies based on trpB was highly significant: Most nodes resolved by trpB corresponded to nodes resolved by the pooled aphid genes. Furthermore, no nodes were both inconsistent between the trees and strongly supported in both trees. Two kinds of analyses testing the null hypothesis of perfect congruence between pairwise combinations of datasets and tree topologies were performed: the Kishino-Hasegawa test and the likelihood-ratio test. Both tests indicated significant disagreement among most pairwise combinations of mitochondrial, nuclear, and symbiont datasets. Because rampant recombination among mitochondrial genomes of different aphid species is unlikely, inaccurate assumptions in the evolutionary models underlying these tests appear to be causing the hypothesis of a shared history to be incorrectly rejected. Moreover, trpB was more consistent with the aphid genes as a set than any single aphid gene was with the others, suggesting that the symbionts show the same phylogeny as the aphids. Overall, analyses support the interpretation that symbionts and aphids have undergone strict cospeciation, with no horizontal transmission of symbionts even among closely related, ecologically similar aphid hosts.