Bootstrap confidence levels for phylogenetic trees

Evolutionary trees are often estimated from DNA or RNA sequence data. How much confidence should we have in the estimated trees? In 1985, Felsenstein [Felsenstein, J. (1985) Evolution 39, 783–791] suggested the use of the bootstrap to answer this question. Felsenstein’s method, which in concept is a straightforward application of the bootstrap, is widely used, but has been criticized as biased in the genetics literature. This paper concerns the use of the bootstrap in the tree problem. We show that Felsenstein’s method is not biased, but that it can be corrected to better agree with standard ideas of confidence levels and hypothesis testing. These corrections can be made by using the more elaborate bootstrap method presented here, at the expense of considerably more computation.

Bootstrap confidence levels for phylogenetic trees.

Evolutionary trees are often estimated from DNA or RNA sequence data. How much confidence should we have in the estimated trees? In 1985, Felsenstein [Felsenstein, J. (1985) Evolution 39, 783-791] suggested the use of the bootstrap to answer this question. Felsenstein's method, which in concept is a straightforward application of the bootstrap, is widely used, but has been criticized as biased in the genetics literature. This paper concerns the use of the bootstrap in the tree problem. We show that Felsenstein's method is not biased, but that it can be corrected to better agree with standard ideas of confidence levels and hypothesis testing. These corrections can be made by using the more elaborate bootstrap method presented here, at the expense of considerably more computation.

Gene content phylogeny of herpesviruses

Clusters of orthologous groups [COGs; Tatusov, R. L., Koonin, E. V. & Lipman, D. J. (1997) Science 278, 631–637] were identified for a set of 13 completely sequenced herpesviruses. Each COG represented a family of gene products conserved across several herpes genomes. These families were defined without using an arbitrary threshold criterion based on sequence similarity. The COG technique was modified so that variable stringency in COG construction was possible. High stringencies identify a core set of highly conserved genes. Varying COG stringency reveals differences in the degree of conservation between functional classes of genes. The COG data were used to construct whole-genome phylogenetic trees based on gene content. These trees agree well with trees based on other methods and are robust when tested by bootstrap analysis. The COG data also were used to construct a reciprocal tree that clustered genes with similar phylogenetic profiles. This clustering may give clues to genes with related functions or with related histories of acquisition and loss during herpesvirus evolution.

Compact stellarators with modular coils

Compact stellarator designs with modular coils and only two or three field periods are now available; these designs have both good stability and quasiaxial symmetry providing adequate transport for a magnetic fusion reactor. If the bootstrap current assumes theoretically predicted values a three field period configuration is optimal, but if that net current turns out to be lower, a device with two periods and just 12 modular coils might be better. There are also attractive designs with quasihelical symmetry and four or five periods whose properties depend less on the bootstrap current. Good performance requires that there be a satisfactory magnetic well in the vacuum field, which is a property lacking in a stellarator-tokamak hybrid that has been proposed for a proof of principle experiment. In this paper, we present an analysis of stability for these configurations that is based on a mountain pass theorem asserting that, if two solutions of the problem of magnetohydrodynamic equilibrium can be found, then there has to be an unstable solution. We compare results of our theory of equilibrium, stability, and transport with recently announced measurements from the large LHD experiment in Japan.

Phylogenetic relationships among group II intron ORFs

Group II introns are widely believed to have been ancestors of spliceosomal introns, yet little is known about their own evolutionary history. In order to address the evolution of mobile group II introns, we have compiled 71 open reading frames (ORFs) related to group II intron reverse transcriptases and subjected their derived amino acid sequences to phylogenetic analysis. The phylogenetic tree was rooted with reverse transcriptases (RTs) of non-long terminal repeat retroelements, and the inferred phylogeny reveals two major clusters which we term the mitochondrial and chloroplast-like lineages. Bacterial ORFs are mainly positioned at the bases of the two lineages but with weak bootstrap support. The data give an overview of an apparently high degree of horizontal transfer of group II intron ORFs, mostly among related organisms but also between organelles and bacteria. The Zn domain (nuclease) and YADD motif (RT active site) were lost multiple times during evolution. Differences in domain structures suggest that the oldest ORFs were concise, while the ORF in the mitochondrial lineage subsequently expanded in three locations. The data are consistent with a bacterial origin for mobile group II introns.

On the origin of and phylogenetic relationships among living amphibians

The phylogenetic relationships among the three orders of modern amphibians (Caudata, Gymnophiona, and Anura) have been estimated based on both morphological and molecular evidence. Most morphological and paleontological studies of living and fossil amphibians support the hypothesis that salamanders and frogs are sister lineages (the Batrachia hypothesis) and that caecilians are more distantly related. Previous interpretations of molecular data based on nuclear and mitochondrial rRNA sequences suggested that salamanders and caecilians are sister groups to the exclusion of frogs. In an attempt to resolve this apparent conflict, the complete mitochondrial genomes of a salamander (Mertensiella luschani) and a caecilian (Typhlonectes natans) were determined (16,656 and 17,005 bp, respectively) and compared with previously published sequences from a frog (Xenopus laevis) and several other groups of vertebrates. Phylogenetic analyses of the mitochondrial data supported with high bootstrap values the monophyly of living amphibians with respect to other living groups of tetrapods, and a sister group relationship of salamanders and frogs. The lack of phylogenetically informative sites in the previous rRNA data sets (because of its shorter size and higher among-site rate variation) likely explains the discrepancy between our results and those based on previous molecular data. Strong support of the Batrachia hypothesis from both molecule- and morphology-based studies provides a robust phylogenetic framework that will be helpful to comparative studies among the three living orders of amphibians and will permit better understanding of the considerably divergent vertebral, brain, and digit developmental patterns found in frogs and salamanders.

Perspectives on archaeal diversity, thermophily and monophyly from environmental rRNA sequences.

Phylogenetic analysis of ribosomal RNA sequences obtained from uncultivated organisms of a hot spring in Yellowstone National Park reveals several novel groups of Archaea, many of which diverged from the crenarchaeal line of descent prior to previously characterized members of that kingdom. Universal phylogenetic trees constructed with the addition of these sequences indicate monophyly of Archaea, with modest bootstrap support. The data also show a specific relationship between low-temperature marine Archaea and some hot spring Archaea. Two of the environmental sequences are enigmatic: depending upon the data set and analytical method used, these sequences branch deeply within the Crenarchaeota, below the bifurcation between Crenarchaeota and Euryarchaeota, or even as the sister group to Eukaryotes. If additional data confirm either of the latter two placements, then the organisms represented by these ribosomal RNA sequences would merit recognition as a new kingdom, provisionally named "Korarchaeota."

The root of the universal tree and the origin of eukaryotes based on elongation factor phylogeny.

The genes for the protein synthesis elongation factors Tu (EF-Tu) and G (EF-G) are the products of an ancient gene duplication, which appears to predate the divergence of all extant organismal lineages. Thus, it should be possible to root a universal phylogeny based on either protein using the second protein as an outgroup. This approach was originally taken independently with two separate gene duplication pairs, (i) the regulatory and catalytic subunits of the proton ATPases and (ii) the protein synthesis elongation factors EF-Tu and EF-G. Questions about the orthology of the ATPase genes have obscured the former results, and the elongation factor data have been criticized for inadequate taxonomic representation and alignment errors. We have expanded the latter analysis using a broad representation of taxa from all three domains of life. All phylogenetic methods used strongly place the root of the universal tree between two highly distinct groups, the archaeons/eukaryotes and the eubacteria. We also find that a combined data set of EF-Tu and EF-G sequences favors placement of the eukaryotes within the Archaea, as the sister group to the Crenarchaeota. This relationship is supported by bootstrap values of 60-89% with various distance and maximum likelihood methods, while unweighted parsimony gives 58% support for archaeal monophyly.

Randomness and degrees of irregularity.

The fundamental question "Are sequential data random?" arises in myriad contexts, often with severe data length constraints. Furthermore, there is frequently a critical need to delineate nonrandom sequences in terms of closeness to randomness--e.g., to evaluate the efficacy of therapy in medicine. We address both these issues from a computable framework via a quantification of regularity. ApEn (approximate entropy), defining maximal randomness for sequences of arbitrary length, indicating the applicability to sequences as short as N = 5 points. An infinite sequence formulation of randomness is introduced that retains the operational (and computable) features of the finite case. In the infinite sequence setting, we indicate how the "foundational" definition of independence in probability theory, and the definition of normality in number theory, reduce to limit theorems without rates of convergence, from which we utilize ApEn to address rates of convergence (of a deficit from maximal randomness), refining the aforementioned concepts in a computationally essential manner. Representative applications among many are indicated to assess (i) random number generation output; (ii) well-shuffled arrangements; and (iii) (the quality of) bootstrap replicates.

Calculating the probability of multitaxon evolutionary trees: bootstrappers Gambit.

The reconstruction of multitaxon trees from molecular sequences is confounded by the variety of algorithms and criteria used to evaluate trees, making it difficult to compare the results of different analyses. A global method of multitaxon phylogenetic reconstruction described here, Bootstrappers Gambit, can be used with any four-taxon algorithm, including distance, maximum likelihood, and parsimony methods. It incorporates a Bayesian-Jeffreys'-bootstrap analysis to provide a uniform probability-based criterion for comparing the results from diverse algorithms. To examine the usefulness of the method, the origin of the eukaryotes has been investigated by the analysis of ribosomal small subunit RNA sequences. Three common algorithms (paralinear distances, Jukes-Cantor distances, and Kimura distances) support the eocyte topology, whereas one (maximum parsimony) supports the archaebacterial topology, suggesting that the eocyte prokaryotes are the closest prokaryotic relatives of the eukaryotes.