The Exact Distribution of the Anderson-Kannemann Statistic

The Anderson-Kannemann test is a rank test for treatment effects in a randomized block design with K treatments and N blocks. In this paper, an algorithm for computing the exact distribution of the Anderson-Kannemann test statistic under the null hypothesis is deduced. Then, the exact distribution is compared with the asymptotic χ²-distribution, and it is shown that the exact distribution is approximated fairly well by the asymptotic distribution. Tables of the exact distribution are given for K = 3, N = 3(1)15; K = 4, N = 3(1)11; K = 5, N = 3(1)7; and K = 6, N = 3(1)5.     

The Exact Evaluation of 2-way Cross-classifications: The Combinatory Distribution

A practical methodology is presented for the exact combinatory evaluation of 2-way cross-classifications. The combinatory distribution is based on a test-statistic relating to the information content of an observed table. Several examples of exact evaluation accompany this presentation.     

Molecular Clock Calibrations and Metazoan Divergence Dates

It has recently been argued that living metazoans diverged over 800 million years ago, based on evidence from 22 nuclear genes for such a deep divergence between vertebrates and arthropods (Gu 1998). Two ``internal' calibration points were used. However, only one fossil divergence date (the mammal–bird split) was directly used to calibrate the molecular clock. The second calibration point (the primate–rodent split) was based on molecular estimates that were ultimately also calibrated by the same mammal–bird split. However, the first tetrapods that can be assigned with confidence to either the mammal (synapsid) lineage or the bird (diapsid) lineage are approximately 288 million years old, while the first mammals that can be assigned with confidence to either the primate or the rodent lineages are 65 million years old, or 85 million years old if ferungulates are part of the primate lineage and zhelestids are accepted as ferungulate relatives. Recalibration of the protein data using these fossil dates indicates that metazoans diverged between 791 and 528 million years ago, a result broadly consistent with the palaeontological documentation of the ``Cambrian explosion.' The third, ``external' calibration point (the metazoan–fungal divergence) was similarly problematic, since it was based on a controversial molecular study (which in turn used fossil dates including the mammal–bird split); direct use of fossils for this calibration point gives the absurd dating of 455 million years for metazoan divergences. Similar calibration problems affect another recent study (Wang et al. 1999), which proposes divergences for metazoans of 1000 million years or more: recalibrations of their clock again yields much more recent dates, some consistent with a ``Cambrian explosion' scenario. Molecular clock studies have persuasively argued for the imperfection of the fossil record but have rarely acknowledged that their inferences are also directly based on this same record. Received: 26 January 1999 / Accepted: 14 April 1999     

Divergence and convergence in enzyme evolution

Comparative analysis of the sequences of enzymes encoded in a variety of prokaryotic and eukaryotic genomes reveals convergence and divergence at several levels. Functional convergence can be inferred when structurally distinct and hence non-homologous enzymes show the ability to catalyze the same biochemical reaction. In contrast, as a result of functional diversification, many structurally similar enzyme molecules act on substantially distinct substrates and catalyze diverse biochemical reactions. Here, we present updates on the ATP-grasp, alkaline phosphatase, cupin, HD hydrolase, and N-terminal nucleophile (Ntn) hydrolase enzyme superfamilies and discuss the patterns of sequence and structural conservation and diversity within these superfamilies. Typically, enzymes within a superfamily possess common sequence motifs and key active site residues, as well as (predicted) reaction mechanisms. These observations suggest that the strained conformation (the entatic state) of the active site, which is responsible for the substrate binding and formation of the transition complex, tends to be conserved within enzyme superfamilies. The subsequent fate of the transition complex is not necessarily conserved and depends on the details of the structures of the enzyme and the substrate. This variability of reaction outcomes limits the ability of sequence analysis to predict the exact enzymatic activities of newly sequenced gene products. Nevertheless, sequence-based (super)family assignments and generic functional predictions, even if imprecise, provide valuable leads for experimental studies and remain the best approach to the functional annotation of uncharacterized proteins from new genomes.     

Divergence in a transoceanic circumtropical dragonfly on a remote island

One terrestrial invertebrate that naturally spans the globe and travels vast distances is the dragonfly Pantala flavescens (Fabricius) (Odonata: Libellulidae). Recently, there has been a strong call to compare island with continental biota so as to meaningfully characterize island forms. This is done here. The variation and differences in morphology and behaviour of an African continental (Pietermaritzburg, South Africa) and a remote island population (Easter Island) of P. flavescens was investigated to determine whether the island population was panmictic with the migrant population, or whether it was a founder population. Several morphological characters were measured in both populations, and analysed using PCA, t-tests, coefficients of variation and Chi-square analyses. The continental and island populations were significantly different in body colour, head width and femur length. The island population had reduced hindwings, which were also more asymmetrical than the continental population, suggesting that the island individuals were possibly more genetically and environmentally stressed and had less genetic variation than the continental population. The island population was also more robust and flew lower to the ground than the continental population. There was no significant difference in body weight between the two populations because the migrant population had not begun to build up fat reserves for migration. Females were heavier than males in the continental population because they were carrying eggs. This was not the case in the island population because the individuals were not as mature. Colour was significantly different between the two populations, with island individuals having darker wings and abdomens, yet a lighter synthorax colouring than the continental population. Sexual dimorphism was marked in the abdomen and wing colour of the continental population, yet the island individuals showed more difference between the sexes in morphological characters than in colour. The fact that P. flavescens is the only species of dragonfly on Easter Island, and the great distance of the island from any mainland, suggests infrequent arrival of migrants arriving on the island, with resultant reduced genetic variation. The morphological and behavioural differences between the two populations suggests divergence is occurring.     

The fossil record and estimating divergence times between lineages: Maximum divergene times and the importance of reliable phylogenies

Summary Bounded estimates on divergence times between lineaes are crucial to the calculation of absolute rates of molecular evolution. Upper (minimum) bounds on divergence times are easily estimated based on earliest fossil finds. Lower (maximum) bounds are more difficult to estimate; the age of putative ancestors may be used, though in practice it is virtually impossible to distinguish ancestors from primitive sister groups, which do not, of logical necessit, consitute lower bounds on divergence times. Two relatively new approaches to estimating lower bounds directly assess the incompleteness of the fossil record. The first uses taphonomic control groups to distinguish real absences from nonpreservation, while the second, and probably more powerful, uses the quality of the fossil recored to estimate confidence intervals on the bases of stratigraphic ranges. For some groups, especially vertebrates, the inclusion or exclusion of problematic fossils can dramaticaly affect estimated lower bounds on divergence times, often swamping the uncertainties due to the incompleteness of the fossil record and/or corelation and dating errors. When datable paleogeographic events reflect ancient divisions of faunas, a lower bound on the divergence time of speices within a fauna can be established based on the geologic, rather than fossil, record. The fossil records of hominids, eutherianmammals, echinoids, and geese are used as examples.This article was presented at the C.S.E.O.L. Conferrence on DNA-DNA Hybridization and Evolution, Lake Arrowhead, California, May 11–14, 1989     

On the HIV Incubation Distribution Under AZT Treatment

Assuming some general models for the HIV epidemic, in this paper I derive the HIV incubation distributions under AZT treatment. It is shown that under some conditions, these probability distributions are mixtures of some generalized Gamma distributions and products of generalized Gamma distributions.     

广义柏科主要分类群起源时间的推测

通过构建分子钟对广义柏科主要分类群的起源时间进行探讨。采用相对速率检验法分析广义柏科mat K、rbc L进化速率的稳定性,结果显示rbc L的非同义替代速率只在Pinaceae与Taxodiaceae的分类群及柏科北半球的支系(Cupressoideae)之间通过相对速率检验,而Pinaceae与柏科南半球分支(Callitrodeae)之间没有通过相对速率检验。mar K基因的非同义替代速率在Pinaceae与广义柏科的所有分类群之间通过相对速率检验。根据通过相对速率检验的分类群之间的遗传距离和基因进化速率,计算它们发生分歧的时间。据此推测,杉科的主要分类群Taiwanioideae、Athrotaxidoideae、Sequoioideae与其他分支发生分歧的时间均在侏罗纪,支持现存杉科在侏罗纪就已经建立起来的观点;Cupressaceae(s．s．)的两个支系(亚科)发生分歧的时间在124Ma之前,相当于早白垩世早期,可能由于南北古大陆的完全分离,其祖先居群被分隔成两个亚群,随后各自演化为不同的支系。Callitirodeae、Cupressoideae各属发生分歧的时间也均在白垩纪,表明Cupressaceae(s．s．)在白垩纪就已经建立起来。     

TimeTree 5: An Expanded Resource for Species Divergence Times

We present the fifth edition of the TimeTree of Life resource (TToL5), a product of the timetree of life project that aims to synthesize published molecular timetrees and make evolutionary knowledge easily accessible to all. Using the TToL5 web portal, users can retrieve published studies and divergence times between species, the timeline of a species’ evolution beginning with the origin of life, and the timetree for a given evolutionary group at the desired taxonomic rank. TToL5 contains divergence time information on 137,306 species, 41% more than the previous edition. The TToL5 web interface is now Americans with Disabilities Act-compliant and mobile-friendly, a result of comprehensive source code refactoring. TToL5 also offers programmatic access to species divergence times and timelines through an application programming interface, which is accessible at timetree.temple.edu/api. TToL5 is publicly available at timetree.org.     

Phylogeny and Bayesian divergence time estimations of small-headed flies (Diptera: Acroceridae) using multiple molecular markers

The first formal analysis of phylogenetic relationships among small-headed flies (Acroceridae) is presented based on DNA sequence data from two ribosomal (16S and 28S) and two protein-encoding genes: carbomoylphosphate synthase (CPS) domain of CAD (i.e., rudimentary locus) and cytochrome oxidase I (COI). DNA sequences from 40 species in 22 genera of Acroceridae (representing all three subfamilies) were compared with outgroup exemplars from Nemestrinidae, Stratiomyidae, Tabanidae, and Xylophagidae. Parsimony and Bayesian simultaneous analyses of the full data set recover a well-resolved and strongly supported hypothesis of phylogenetic relationships for major lineages within the family. Molecular evidence supports the monophyly of traditionally recognised subfamilies Philopotinae and Panopinae, but Acrocerinae are polyphyletic. Panopinae, sometimes considered "primitive" based on morphology and host-use, are always placed in a more derived position in the current study. Furthermore, these data support emerging morphological evidence that the type genus Acrocera Meigen, and its sister genus Sphaerops, are atypical acrocerids, comprising a sister lineage to all other Acroceridae. Based on the phylogeny generated in the simultaneous analysis, historical divergence times were estimated using Bayesian methodology constrained with fossil data. These estimates indicate Acroceridae likely evolved during the late Triassic but did not diversify greatly until the Cretaceous.     

Bayes Estimator of Survival Probability from Randomly Censored Observations with Weibull Distribution of Time to Death

This paper deals with Bayes estimation of survival probability when the data are randomly censored. Such a situation arises in case of a clinical trial which extends for a limited period T. A fixed number of patients (n) are observed whose times to death have identical Weibull distribution with parameters β and θ. The maximum times of observation for different patients are also independent uniform variables as the patients arrive randomly throughout the trial. For the joint prior distribution of (β, θ) as suggested by Sinha and Kale (1980, page 137) Bayes estimator of survival probability at time t (0<t<T) has been obtained. Considering squared error loss function it is the mean of the survival probability with respect to the posterior distribution of (β, θ). This estimator is then compared with the maximum likelihood estimator, by simulation, for various values of β, θ and censoring percentage. The proposed estimator is found to be better under certain conditions.     

Phylogeny and Divergence Times of Gymnosperms Inferred from Single-Copy Nuclear Genes

Phylogenetic reconstruction is fundamental to study evolutionary biology and historical biogeography. However, there was not a molecular phylogeny of gymnosperms represented by extensive sampling at the genus level, and most published phylogenies of this group were constructed based on cytoplasmic DNA markers and/or the multi-copy nuclear ribosomal DNA. In this study, we use LFY and NLY, two single-copy nuclear genes that originated from an ancient gene duplication in the ancestor of seed plants, to reconstruct the phylogeny and estimate divergence times of gymnosperms based on a complete sampling of extant genera. The results indicate that the combined LFY and NLY coding sequences can resolve interfamilial relationships of gymnosperms and intergeneric relationships of most families. Moreover, the addition of intron sequences can improve the resolution in Podocarpaceae but not in cycads, although divergence times of the cycad genera are similar to or longer than those of the Podocarpaceae genera. Our study strongly supports cycads as the basal-most lineage of gymnosperms rather than sister to Ginkgoaceae, and a sister relationship between Podocarpaceae and Araucariaceae and between Cephalotaxaceae-Taxaceae and Cupressaceae. In addition, intergeneric relationships of some families that were controversial, and the relationships between Taxaceae and Cephalotaxaceae and between conifers and Gnetales are discussed based on the nuclear gene evidence. The molecular dating analysis suggests that drastic extinctions occurred in the early evolution of gymnosperms, and extant coniferous genera in the Northern Hemisphere are older than those in the Southern Hemisphere on average. This study provides an evolutionary framework for future studies on gymnosperms.     

Early Metazoan Divergence Was About 830 Million Years Ago

From a total of 22 nuclear genes, we estimate that the divergence time between Drosophila and vertebrates was about 830 million years ago (mya), which is significantly (1% level) earlier than the Cambrian explosion indicated by the early triploblastic fossils (<600 mya). Received: 21 November 1997 / Accepted: 18 February 1998     

Estimation of divergence times in cnidarian evolution based on mitochondrial protein-coding genes and the fossil record

The phylum Cnidaria is comprised of remarkably diverse and ecologically significant taxa, such as the reef-forming corals, and occupies a basal position in metazoan evolution. The origin of this phylum and the most recent common ancestors (MRCAs) of its modern classes remain mostly unknown, although scattered fossil evidence provides some insights on this topic. Here, we investigate the molecular divergence times of the major taxonomic groups of Cnidaria (27 Hexacorallia, 16 Octocorallia, and 5 Medusozoa) on the basis of mitochondrial DNA sequences of 13 protein-coding genes. For this analysis, the complete mitochondrial genomes of seven octocoral and two scyphozoan species were newly sequenced and combined with all available mitogenomic data from GenBank. Five reliable fossil dates were used to calibrate the Bayesian estimates of divergence times. The molecular evidence suggests that cnidarians originated 741 million years ago (Ma) (95% credible region of 686-819), and the major taxa diversified prior to the Cambrian (543 Ma). The Octocorallia and Scleractinia may have originated from radiations of survivors of the Permian-Triassic mass extinction, which matches their fossil record well.     

Comments on "Improving estimates of the basic reproductive ratio: using both the mean and the dispersal of transition times"

Comments on Heffernan, J. M., Wahl, L. M. (2006). Improving estimates of the basic reproductive ratio: Using both the mean and the dispersal of transition times. Theoretical Population Biology, 70, 135-145.     

一个适于最大似然法估计物种分化年代的进化速率平滑近似方法

众所周知 ,物种分化年代的估计对分子钟 (进化速率恒定 )假定很敏感。另一方面 ,在远缘物种 (例如哺乳纲不同目的动物 )的比较中 ,分子钟几乎总是不成立的。这样在估计分化时间时考虑不同进化区系的速率差异至为重要。最大似然法可以很自然地考虑这种速率差异 ,并且可以同时分析多个基因位点的资料以及同时利用多重化石校正数据。以前提出的似然法需要研究者将进化树的树枝按速率分组 ,本文提出一个近似方法以使这个过程自动化。本方法综合了以前的似然法、贝斯法及近似速率平滑法的一些特征。此外 ,还对算法加以改进 ,以适应综合数据分析时某些基因在某些物种中缺乏资料的情形。应用新提出的方法来分析马达加斯加的倭狐猴的分化年代 ,并与以前的似然法及贝斯法的分析进行了比较     

Fungi Evolution Revisited: Application of the Penalized Likelihood Method to a Bayesian Fungal Phylogeny Provides a New Perspective on Phylogenetic Relationships and Divergence Dates of Ascomycota Groups

The depiction of evolutionary relationships within phylum Ascomycota is still controversial because of unresolved branching orders in the radiation of major taxa. Here we generated a dataset of 166 small subunit (18S) rDNA sequences, representative of all groups of Fungi and used as input in a Bayesian phylogenetic analysis. This phylogeny suggests that Discomycetes are a basal group of filamentous Ascomycetes and probably maintain ancestor characters since their representatives are intermingled among other filamentous fungi. Also, we show that the evolutionary rate heterogeneity within Ascomycota precludes the assumption of a global molecular clock. Accordingly, we used the penalized likelihood method, and for calibration we included a 400 million-year-old Pyrenomycete fossil considering two distinct scenarios found in the literature, one with an estimated date of 1576 Myr for the plant–animal–fungus split and the other with an estimated date of 965 Myr for the animal–fungus split. Our data show that the current classification of the fossil as a Pyrenomycete is not compatible with the second scenario. Estimates under the first scenario are older than dates proposed in previous studies based on small subunit rDNA sequences but support estimates based on multiprotein analysis, suggesting that the radiation of the major Ascomycota groups occurred into the Proterozoic era. Reviewing Editor: Dr. Nicolas Galtier