Rates of single-copy DNA evolution in herons

DNA-DNA hybridization was used to discover the extent of single-copy DNA similarity among 13 species of herons and one ibis. Genetic distances among taxa were summarized as Tm values in a folded matrix. From this matrix, trees with the same branching pattern were constructed by least squares under one of two assumptions: (1) that sister branches are equal in length and (2) that sister branches are not necessarily equal in length. The residual sums of squares of these trees were compared by F-test to see whether the branches of the tree built under assumption (2) fit the matrix data significantly better than those of the tree built under assumption (1). By this method the existence of different rates of DNA evolution in different heron lineages was established. Bittern single-copy DNA has evolved at a rate approximately 25% faster, and boat-billed heron (Cochearius) and rufescent tiger heron (Tigrisoma lineatum) DNA has evolved approximately 19% slower, than that of day and night herons. It appears that the differences in rates of DNA evolution may increase proportionally with genealogical distance.      

Speciational Evolution: a Phylogenetic Test With Allozymes in Sceloporus (Reptilia)

Abstract— The potential role of speciation in accelerating evolutionary divergence remains controversial. Earlier tests based on genetic and morphologic distances which indicated an absence of speciational evolution rely on problematic assumptions. We provide a phylogenetic test in which amounts of discrete character change relative to an outgroup are compared between sister taxa. Although this test is constrained by a need to assume similar extinction rates in groups compared, it provides conceptual improvements regarding monophyly, equal age of taxa, and distribution of homoplasy. Based on analysis of 68 informative allozyme characters for 19 lizard species in the genus Sceloporus , significant speciational evolution and punctuational change is, at least, a viable explanation for the distribution of observed character changes.     

Distance measures in terms of substitution processes.

Phylogenetic reconstruction from DNA or amino acid sequences relies heavily on suitable distance measures. A number of new distance measures (asynchronous, LogDet, and paralinear distances) which possess the desired property of tree additivity under fairly general models of sequence evolution have been proposed recently, but they are not well understood from a mechanistic point of view. We review them here in a unifying framework, which is the substitution process in continuous time. The emerging interpretation will also clarify the relationship among these distance measures. We also tackle situations with site-to-site variation of substitution rates which is well known to cause non-additive distances and inconsistent branch lengths. For homogeneous, stationary, time-reversible models, this may be repaired provided that the distribution of rates is known. In contrast, we will show that, for non-stationary models, different tree topologies may produce identical joint distributions of letters in pairs of sequences, given the same distribution of rates. This precludes the existence of any tree-additive pairwise distance measure.     

The Applicability of Ordinary Least Squares to Consistently Short Distances between Taxa in Phylogenetic Tree Construction and the Normal Distribution Test Consequences

Short phylogenetic distances between taxa occur, for example, in studies on ribosomal RNA-genes with slow substitution rates. For consistently short distances, it is proved that in the completely singular limit of the covariance matrix ordinary least squares (OLS) estimates are minimum variance or best linear unbiased (BLU) estimates of phylogenetic tree branch lengths. Although OLS estimates are in this situation equal to generalized least squares (GLS) estimates, the GLS chi-square likelihood ratio test will be inapplicable as it is associated with zero degrees of freedom. Consequently, an OLS normal distribution test or an analogous bootstrap approach will provide optimal branch length tests of significance for consistently short phylogenetic distances. As the asymptotic covariances between branch lengths will be equal to zero, it follows that the product rule can be used in tree evaluation to calculate an approximate simultaneous confidence probability that all interior branches are positive.     

Phylogenetic relationships and rates of allozyme evolution among the lineages of sceloporine sand lizards

Parsimony analysis of characters derived from an electrophoretic survey of allozyme variation in the sceloporine sand lizards indicates that Uma is outside of a clade formed by the rest of the sand lizards and that Cophosaurus and Holbrookia share a more recent common ancestor with one another than either does with Callisaurus. Previous electrophoretic studies used phenetic clustering based on genetic distance data to assess relationships among these taxa. The resulting dendrograms were used to argue that Holbrookia is the sister group of all other sand lizards and that Callisaurus and Cophosaurus are sister taxa. When reanalysed using parsimony methods, the data from these previous studies are found to support the conclusions of the present study, namely, that Uma rather than Holbrookia is the sister group of all other sand lizards and that Cophosaurus is the sister taxon of Holbrookia rather than of Callisaurus. Relative rate tests indicate that the incongruencies between branching diagrams derived from phenetic clustering of genetic distances versus those derived from parsimony analysis of electrophoretic characters are attributable to increased rates of protein evolution in the Holbrookia lineage.     

Molecular systematics of cytochrome oxidase I and 16S from Neochlamisus leaf beetles and the importance of sampling.

If a gene tree is to be judiciously used for inferring the histories of closely related taxa, (1) its topology must be sufficiently resolved and robust that noteworthy phylogenetic patterns can be confidently documented, and (2) sampling of species, populations, and pertinent biological variation must be sufficiently broad that otherwise misleading sources of genetic variation can be detected. These principles are illustrated by the complex gene tree of Neochlamisus leaf beetles that I reconstructed using 90,000 bp of cytochrome oxidase I (COI) and 16S mitochondrial DNA (mtDNA) sequences from over 100 specimens. Cytochrome oxidase I haplotypes varied up to 25.1% within Neochlamisus and up to 11.1% within the gibbosus species group, while exhibiting very low A + T bias for insect mtDNA (63%), low transition saturation, and conservative patterns of amino acid variation. 16S exhibited lower sequence divergences and greater A + T bias and transition saturation than COI, and substitutions were more constrained in stems than in loops. Comparisons with an earlier study of Ophraella leaf beetles highlighted conservative and labile elements of molecular evolution across genes and taxa. Cytochrome oxidase I parsimony and neighbor-joining analyses strongly supported a robust mtDNA genealogy that revealed the monophyly of Neochlamisus and of the gibbosus species group. Phylogeographic relationships suggested that the eastern U.S. gibbosus group derives from southwestern velutinus group ancestors. Haplotypes from individual velutinus group species clustered monophyletically, as expected. However, haplotypes from each of several gibbosus group taxa were polyphyletically distributed, appearing in divergent parts of the tree. 16S provided a less-resolved gibbosus group topology that was congruent with the COI tree and corroborated patterns of mitochondrial polyphyly. By subsampling haplotypes corresponding to particular species, populations, and ecological variants of gibbosus group taxa, I demonstrate that recovered topologies and genetic distances vary egregiously according to sampling regime. This study thus documents the potentially dire consequences of inadequate sampling when inferring the evolutionary history of closely related and mitochondrially polyphyletic taxa.     

Bootstrap approaches to estimating confidence intervals for molecular dissimilarities and resultant trees

Varied approaches to estimating confidence intervals for immunological and hybridization distances can be uniformly applied to any matrix of distances. One procedure bootstraps the pairwise dissimilarities between the distances of every pair of taxa to all others, creating a derived matrix of distances for which dispersions can be estimated. Another approach bootstraps the sample of differences between pairwise homologous branch lengths concerning each pair of taxa and between asymmetric halves of the matrix, to find a standard error of the dispersions. This allows comparison of the robustness of trees among different sources of data. DNA hybridization, transferrin immunology and protein immunodiffusion matrices all yield much the same result once standard deviations of dissimilarities are acknowledged: namely, unresolvable trichotomies among the human-chimp-gorilla clade and among this clade with orang and gibbon; conventional relationships among hominoids, cercopithecoids, ceboids and strepsirhines; and a polychotomy among anthropoids, strepsirhines, tarsiers, tupaiids and dermopterans.     

Accounting for variation of substitution rates through time in Bayesian phylogeny reconstruction of Sapotoideae (Sapotaceae)

We used Bayesian phylogenetic analysis of 5 kb of chloroplast DNA data from 68 Sapotaceae species to clarify phylogenetic relationships within Sapotoideae, one of the two major clades within Sapotaceae. Variation in substitution rates through time was shown to be a very important aspect of molecular evolution for this data set. Relative rates tests indicated that changes in overall rate have taken place in several lineages during the history of the group and Bayes factors strongly supported a covarion model, which allows the rate of a site to vary over time, over commonly used models that only allow rates to vary across sites. Rate variation over time was actually found to be a more important model component than rate variation across sites. The covarion model was originally developed for coding gene sequences and has so far only been tested for this type of data. The fact that it performed so well with the present data set, consisting mainly of data from noncoding spacer regions, suggests that it deserves a wider consideration in model based phylogenetic inference. Repeatability of phylogenetic results was very difficult to obtain with the more parameter rich models, and analyses with identical settings often supported different topologies. Overparameterization may be the reason why the MCMC did not sample from the posterior distribution in these cases. The problem could, however, be overcome by using less parameter rich evolutionary models, and adjusting the MCMC settings. The phylogenetic results showed that two taxa, previously thought to belong in Sapotoideae, are not part of this group. Eberhardtia aurata is the sister of the two major Sapotaceae clades, Chrysophylloideae and Sapotoideae, and Neohemsleya usambarensis belongs in Chrysophylloideae. Within Sapotoideae two clades, Sideroxyleae and Sapoteae, were strongly supported. Bayesian analysis of the character history of some floral morphological traits showed that the ancestral type of flower in Sapotoideae may have been characterized by floral parts (sepals, petals, stamens, and staminodes) in single whorls of five, entire corolla lobes, and seeds with an adaxial hilum.     

Rates of molecular evolution and the fraction of nucleotide positions free to vary

Summary Selective constraints on DNA sequence change were incorporated into a model of DNA divergence by restricting substitutions to a subset of nucleotide positions. A simple model showed that both mutation rate and the fraction of nucleotide positions free to vary are strong determinants of DNA divergence over time.When divergence between two species approaches the fraction of positions free to vary, standard methods that correct for multiple mutations yield severe underestimates of the number of substitutions per site. A modified method appropriate for use with DNA sequence, restriction site, or thermal renaturation data is derived taking this fraction into account. The model also showed that the ratio of divergence in two gene classes (e.g., nuclear and mitochondrial) may vary widely over time even if the ratio of mutation rates remains constant.DNA sequence divergence data are used increasingly to detect differences in rates of molecular evolution. Often, variation in divergence rate is assumed to represent variation in mutation rate. The present model suggests that differing divergence rates among comparisons (either among gene classes or taxa) should be interpreted cautiously. Differences in the fraction of nucleotide positions free to vary can serve as an important alternative hypothesis to explain differences in DNA divergence rates.     

外群选择对隧蜂科（膜翅目：蜜蜂总科）系统重建的影响

外群用于给树附根和推断祖先性状状态。通常,来自内群的姐妹群中的多个分类单元被共同选择作为外群。为了在经验上验证这一方法, 我们采用了3种外群选择策略： 姐妹群中的单一分类单元, 姐妹群中的多个分类单元和连续姐妹群中的多个分类单元。以隧蜂科（膜翅目： 蜜蜂总科）的系统发育重建为例, 我们评估了这3种策略对树拓扑结构的影响, 包括最大似然树、 最大简约树和贝叶斯树。初步结果表明： 相比其他两种策略, 采用姐妹群中的多个分类单元作为外群更有利于系统发育重建得到现已被广泛认可的隧蜂科系统发育关系; 相比最大似然法和贝叶斯法, 虽然隧蜂科系统发育关系没有被很好地解决, 但最大简约法在不同外群选择策略下得到了较为一致的拓扑结构     

Variation in modes and rates of evolution in nuclear and mitochondrial ribosomal DNA in the mushroom genus Amanita (Agaricales, Basidiomycota): phylogenetic implications

Modes and rates of molecular evolution, and congruence and combinability for phylogenetic reconstruction, of portions of the nuclear large ribosomal subunit (nLSU-rDNA) and mitochondrial small subunit (mtSSU-rDNA) genes were investigated in the mushroom genus Amanita. The AT content was higher in the mtSSU-rDNA than in the nLSU-rDNA. A transition bias in which AT substitutions were as frequent as transitions was present in the mtSSU-rDNA but not in the nLSU-rDNA. Among-sites rate variation in nucleotide substitutions at variable sites was present in the nLSU-rDNA but not in the mtSSU-rDNA. Likelihood ratio tests indicated very different models of evolution for the two molecules. A molecular clock could be rejected for both data sets. Rates of molecular evolution in the two molecules were uncoupled: faster evolutionary rates in the mtSSU-rDNA and nLSU-rDNA were not observed for the same taxa. In separate phylogenetic analyses, the nLSU-rDNA data set had higher phylogenetic resolution. The partition homogeneity test and statistical bootstrap support for branches indicated absence of conflict in the phylogenetic signal in the two data sets; however, tree topologies produced from the separate data sets were not congruent. Heterogeneity in modes and rates of evolution in the two molecules pose difficulties for a combined analysis of the two data sets: the use of equally weighted parsimony is not fully satisfactory when rate heterogeneity is present, and it is impractical to determine a model for maximum-likelihood analysis that fits simultaneously two heterogeneous data sets. Overall topologies produced from either the separated or the combined analyses using various tree reconstruction methods were identical for nearly all statistically significant branches.     

A Phylogenomic Approach to Vertebrate Phylogeny Supports a Turtle-Archosaur Affinity and a Possible Paraphyletic Lissamphibia

In resolving the vertebrate tree of life, two fundamental questions remain: 1) what is the phylogenetic position of turtles within amniotes, and 2) what are the relationships between the three major lissamphibian (extant amphibian) groups? These relationships have historically been difficult to resolve, with five different hypotheses proposed for turtle placement, and four proposed branching patterns within Lissamphibia. We compiled a large cDNA/EST dataset for vertebrates (75 genes for 129 taxa) to address these outstanding questions. Gene-specific phylogenetic analyses revealed a great deal of variation in preferred topology, resulting in topologically ambiguous conclusions from the combined dataset. Due to consistent preferences for the same divergent topologies across genes, we suspected systematic phylogenetic error as a cause of some variation. Accordingly, we developed and tested a novel statistical method that identifies sites that have a high probability of containing biased signal for a specific phylogenetic relationship. After removing putatively biased sites, support emerged for a sister relationship between turtles and either crocodilians or archosaurs, as well as for a caecilian-salamander sister relationship within Lissamphibia, with Lissamphibia potentially paraphyletic.     

Rate and mode differences between nuclear and mitochondrial small-subunit rRNA genes in mushrooms.

Sequences from homologous regions of the nuclear and mitochondrial small-subunit rRNA genes from 10 members of the mushroom order Boletales were used to construct evolutionary trees and to compare the rates and modes of evolution. Trees constructed independently for each gene by parsimony and tested by bootstrap analysis have identical topologies in all statistically significant branches. Examination of base substitutions revealed that the nuclear gene is biased toward C-T transitions and that the distribution of transversions in the mitochondrial gene is strongly effected by an A-T bias. When only homologous regions of the two genes were compared, base substitutions per nucleotide were roughly 16-fold greater in the mitochondrial gene. The difference in the frequency of length mutations was at least as great but was impossible to estimate accurately because of their absence in the nuclear gene. Maximum likelihood was used to show that base-substitution rates vary dramatically among the branches. A significant part of the rate inconstancy was caused by an accelerated nuclear rate in one branch and a retarded mitochondrial rate in a different branch. A second part of the rate variability involved a consistent inconstancy: short branches exhibit ratios of mitochondrial to nuclear divergences of less than 1, while longer branches had ratios of approximately 4:1-8:1. This pattern suggests a systematic error in the branch length calculation. The error may be related to the simplicity of the divergence estimates, which assumes that all base positions have an equal probability of change.     

Body size effects and rates of cytochrome b evolution in tube-nosed seabirds

Variation in rates of molecular evolution now appears to be widespread. The demonstration that body size is correlated with rates of molecular evolution suggests that physiological and ecological factors may be involved in molecular rate variation, but large-scale comparative studies are still lacking. Here, we use complete cytochrome b sequences from 85 species of tube-nosed seabirds (order Procellariiformes) and 5 outgroup species of penguins (order Sphenisciformes) to test for an association between body mass and rates of molecular evolution within the former avian order. Cladistic analysis of the 90 sequences estimates a phylogeny largely consistent with the traditional taxonomy of the Procellariiformes. The Diomedeidae, Procellariidae, and Pelecanoididae are monophyletic, while the Hydrobatidae are basal and paraphyletic. However, the two subfamilies within the Hydrobatidae (Hydrobatinae and Oceanitinae) are monophyletic. A likelihood ratio test detects significant deviation from clocklike evolution in our data. Using a sign test for an association between body mass and branch length in the seabird phylogeny, we find that larger taxa tend to have shorter terminal branch lengths than smaller taxa. This observation suggests that rates of mitochondrial DNA evolution are slower for larger taxa. Rate calibrations based on the fossil record reveal concordant body size effects. We interpret these results as evidence for a metabolic rate effect, as the species in this order exhibit large differences in metabolic rates, which are known to be highly correlated with body mass in this group. Our results support previous findings of body size effects and show that this effect can be significant even within a single avian order. This suggests that even lineage-specific molecular clocks may not be tenable if calibrations involve taxa with different metabolic rates.      

Phylogeny of the Brachytheciaceae (Bryophyta) based on morphology and sequence level data

Brachytheciaceae is often considered a taxonomically difficult group of mosses. For example, morphological variation has led to difficulty in generic delimitation. We used DNA sequence data (chloroplast psbT‐H and trnL‐F and nuclear ITS2) together with morphology (63 characters) to examine the relationships within this family. The combined unaligned length of the DNA sequences used in the phylogenetic analyses varied between 1277 and 1343 bp. For phylogeny reconstruction we performed direct optimization, as implemented in POY. Analyses were performed with three different gap costs and the morphological data partition was weighted both: (1) equal to gap cost, and (2) with a weight of one. The utility of sensitivity analysis has recently been cast into doubt; hence in this study it was performed only to explore the effects of weighting on homology statements and topologies and to enable more detailed comparisons between earlier studies utilizing the direct optimization method. The wide sequence length variation of non‐coding ITS2 sequences resulted in character optimizations (i.e., “alignments”) of very different lengths when various gap costs were applied. Despite this variation, the topologies of equally parsimonious trees remained fairly stable. The inclusion of several outgroups, instead of only one, was observed to increase the congruence between data sets and to slightly increase the resolution. An inversion event in the 9 bp loop region in the chloroplast psbT‐N spacer in mosses has been postulated to include only uninformative variation, thus possibly negatively impacting the phylogeny reconstruction. Despite this inversion, its variation within Brachytheciaceae was clearly congruent with information from other sources, but inclusion of these 9 bp in the analysis had only a minor effect on the phylogenetic results. In the most parsimonious topology, which was obtained with equal weighting of all data, Meteoriaceae and Brachytheciaceae were resolved as monophyletic sister groups, which had recently been suggested based on a few shared morphological characters. Our study revealed some new generic relationships within the Brachytheciaceae, which are discussed in light of the morphological characters traditionally used for generic delimitation.     

A mitogenomic timescale for birds detects variable phylogenetic rates of molecular evolution and refutes the standard molecular clock

Current understanding of the diversification of birds is hindered by their incomplete fossil record and uncertainty in phylogenetic relationships and phylogenetic rates of molecular evolution. Here we performed the first comprehensive analysis of mitogenomic data of 48 vertebrates, including 35 birds, to derive a Bayesian timescale for avian evolution and to estimate rates of DNA evolution. Our approach used multiple fossil time constraints scattered throughout the phylogenetic tree and accounts for uncertainties in time constraints, branch lengths, and heterogeneity of rates of DNA evolution. We estimated that the major vertebrate lineages originated in the Permian; the 95% credible intervals of our estimated ages of the origin of archosaurs (258 MYA), the amniote-amphibian split (356 MYA), and the archosaur-lizard divergence (278 MYA) bracket estimates from the fossil record. The origin of modern orders of birds was estimated to have occurred throughout the Cretaceous beginning about 139 MYA, arguing against a cataclysmic extinction of lineages at the Cretaceous/Tertiary boundary. We identified fossils that are useful as time constraints within vertebrates. Our timescale reveals that rates of molecular evolution vary across genes and among taxa through time, thereby refuting the widely used mitogenomic or cytochrome b molecular clock in birds. Moreover, the 5-Myr divergence time assumed between 2 genera of geese (Branta and Anser) to originally calibrate the standard mitochondrial clock rate of 0.01 substitutions per site per lineage per Myr (s/s/l/Myr) in birds was shown to be underestimated by about 9.5 Myr. Phylogenetic rates in birds vary between 0.0009 and 0.012 s/s/l/Myr, indicating that many phylogenetic splits among avian taxa also have been underestimated and need to be revised. We found no support for the hypothesis that the molecular clock in birds "ticks" according to a constant rate of substitution per unit of mass-specific metabolic energy rather than per unit of time, as recently suggested. Our analysis advances knowledge of rates of DNA evolution across birds and other vertebrates and will, therefore, aid comparative biology studies that seek to infer the origin and timing of major adaptive shifts in vertebrates.     

Phylogenetic analysis of slippage-like sequence variation in the V4 rRNA expansion segment in tiger beetles (Cicindelidae)

Sequence variation in the middle part of the small-subunit rRNA was studied for representatives of the major groups in the family Cicindelidae (Coleoptera). All taxa exhibited a much expanded segment in variable region V4 compared to D. melanogaster. This expanded segment was not found in other groups of beetles, including three taxa in the closely related Carabidae. Secondary structure predictions indicate that the expanded segment folds into a single stem-loop structure in all taxa. Despite its structural conservation, the fragment differs strongly in primary sequence, even between closely related sister taxa. Several features of these sequences are consistent with slippage replication as the mechanism that has generated this sequence variation: the level of internal sequence repetition as measured by the relative simplicity factor (RSF), its variation in length between close relatives, and the strong nucleotide bias compared to the remainder of the gene. With few exceptions, there was also a correlation between sequence length and the level of sequence repetition, frequently interpreted as the result of slippage. Phylogenies inferred from the expansion segment were not consistent with existing hypotheses from other molecular data for the group. This indicates that DNA sequences in this region are not homologous throughout the entire Cicindelidae, but it leaves open the possibility that this expansion segment can be used for phylogeny reconstruction within subgroups. The implications of a phylogenetic approach to the understanding of slippage-like evolution are discussed.      

Interrelationships and evolution of the tapeworms (Platyhelminthes: Cestoda)

Interrelationships of the tapeworms (Platyhelminthes: Cestoda) were examined by use of small (SSU) and large (LSU) subunit ribosomal DNA sequences and morphological characters. Fifty new complete SSU sequences were added to 21 sequences previously determined, and 71 new LSU (D1-D3) sequences were determined for the complementary set of taxa representing each of the major lineages of cestodes as currently understood. New sequences were determined for three amphilinidean taxa, but were removed from both alignments due to their excessively high degree of divergence from other cestode sequences. A morphological character matrix coded for supraspecific taxa was constructed by the modification of matrices from recently published studies. Maximum-parsimony (MP) analyses were performed on the LSU, SSU, LSU+SSU, and morphological data partitions, and minimum-evolution (ME) analyses utilizing a general time reversible model of nucleotide substitution including estimates of among-site rate heterogeneity were performed on the molecular data partitions. Resulting topologies were rooted at the node separating the Gyrocotylidea from the Eucestoda. The LSU data were found to be more informative than the SSU data and were more consistent with inferences from morphology, although nodal support was generally weak for most basal nodes. One class of transitions was found to be saturated for comparisons between the most distantly related taxa (gyrocotylideans vs cyclophyllideans and tetrabothriideans). Differences in the topologies resulting from MP and ME analyses were not statistically significant. Nonstrobilate orders formed the basal lineages of trees resulting from analysis of LSU data and morphology. Difossate orders were basal to tetrafossate orders, the latter of which formed a strongly supported clade. A clade including the orders Cyclophyllidea, Nippotaeniidea, and Tetrabothriidea was supported by all data partitions and methods of analysis. Paraphyly of the orders Pseudophyllidea, Tetraphyllidea, and Trypanorhyncha was consistent among the molecular data partitions. Inferences are made regarding a monozoic (nonsegmented) origin of the Eucestoda as represented by the Caryophyllidea and for the evolution of the strobilate and acetabulate/tetrafossate conditions having evolved in a stepwise pattern.     

Determining evolutionary distances from highly diverged nucleic acid sequences: Operator metrics

Summary Operator metrics are explicity designed to measure evolutionary distances from nucleic acid sequences when substitution rates differ greatly among the organisms being compared, or when substitutions have been extensive. Unlike lengths calculated by the distance matrix and parsimony methods, in which substitutions in one branch of a tree can alter the measured length of another branch, lengths determined by operator metrics are not affected by substitutions outside the branch.In the method, lengths (operator metrics) corresponding to each of the branches of an unrooted tree are calculated. The metric length of a branch reconstructs the number of (transversion) differences between sequences at a tip and a node (or between nodes) of a tree. The theory is general and is fundamentally independent of differences in substitution rates among the organisms being compared. Mathematically, the independence has been obtained becuase the metrics are eigen vectors of fundamental equations which describe the evolution of all unrooted trees.Even under conditions when both the distance matrix method or a simple parsimony length method are show to indicate lengths than are an order of magnitude too large or too small, the operator metrics are accurate. Examples, using data calculated with evolutionary rates and branchings designed to confuse the measurement of branch lengths and to camouflage the topology of the true tree, demonstrate the validity of operator metrics. The method is robust. Operator metric distances are easy to calculated, can be extended to any number of taxa, and provide a statistical estimate of their variances.The utility of the method is demonstrated by using it to analyze the origins and evolutionary of chloroplasts, mitochondria, and eubacteria.