The Matched Pairs Problem with Exponential Variates

Two classes of tests for the hypothesis of bivariate symmetry are studied. For paired exponential survival times (t_1j, t_2j), the classes of tests are those based on t_1j-t_2j and those based on log t_1j–log t_2j. For each class the sign, signed ranks, t and likelihood ratio tests are compared via Pitman's criterion of asymptotic relative efficiency (ARE). For tests based on t_1j — t_2j, it is found that: (1) the efficacy of the paired t depends on the coefficient of variation (CV) of the pair means, (2) the signed rank test has the same ARE to the sign test as for the usual location problem. For tests based on log t_1j — log t_2j, the ARE comparisons reduce to the well-known results for the one-sample location problem for samples from a logistic density. Hence, the signed rank test is asymptotically efficient. Furthermore, analyses based on log t_1j — log t_2j are not complicated by the underlying pairing mechanism.     

Reconstruction of ancestral sequences by the inferential method,a tool for protein engineering studies

This paper describes the inferential method, an approach for reconstructing protein and nucleotide sequences of ancestral species, starting from known, homologous, contemporary sequences. The method requires knowledge of the topology of the phylogenetic tree, whose nodes are the species to whom the reconstructed sequences belong.The method has been tested by computer simulation of speciation and nucleotide substitutions, starting from a single ancestral sequence, and by subsequent reconstruction of nodal sequences. Results have shown that reconstructions obtained by the inferential method are affected by limited error frequencies, which (1) are proportional to the squares of nucleotide substitution rates and of internodal distances, and (2) are little influenced by non-uniformity of transformation rates of nucleotides.Furthermore, good agreement of the results has been obtained by comparing protein-sequence reconstructions carried out with the inferential method with those obtained using the maximum parsimony method in two different cases: e.g., a reconstruction of simulated sequences and a reconstruction of mammalian ribonuclease sequences.Abbreviations used MP maximum parsimony method - ML maximum likelihood method - IM inferential method - MY millions of years - N-tree natural-like phylogenetic tree - E-tree equibranched phylogenetic tree - EA percentage number of erroneous amino acids in a reconstructed sequence - EC percentage number of erroneous codons in a reconstructed sequence - t _n time interval between a P- and its - F-sequence nucleotides and amino acids are indicated by their I.U.B. codes (N.C.-I.U.B., 1985) Correspondence to: A. Di Donato     

Consistency of the Asymptotic Quasi-Likelihood Estimate on Linear Models

Consider a model y_t = f_t(θ) + M_t, 0 ⩽ t ⩽ T where θ∈ Θ in an unknown parameter, f_t(θ) is a linear predictable process, M_t is a martingale difference, and the nature of E(M²_t/ℱ_t—1) is unknown. This paper presents an estimating procedure for θ based on the asymptotic quasi-likelihood methodology. Conditions under which the asymptotic quasi-likelihood estimate converges to the true parameter θ₀ are discussed. This method is applied to several simulated examples, and estimates of the unknown parameter are obtained by means of a two-stage technique. Comparison is made between the estimates obtained via this method and those obtained via the ordinary least squares method. Discussion is provided on the application of the model.     

Convergence to Normality of the Asymptotic Quasi‐Score Function on a Linear Model

The asymptotic quasi‐likelihood method is considered for the model y_t = f_t(θ) + M_t, t = 0,1, …,T where f_tθ) is a linear predictable process of the parameter of interest θ, M_t is a martingale difference, and the nature of E(M_t² | ℱ_t–1) is unknown. This paper is concerned with the limiting distribution of the asymptotic quasi‐score function of such a model. Confidence intervals and hypothesis testing of θ is derived from the limiting distribution. Comparison is made between the estimates obtained through this method and those obtained through the least squares method.     

Extensive Amplification and Transposition of a Novel Repetitive Element, Xstir, Together with Its Terminal Inverted Repeat in the Evolution of Xenopus

A DNA fragment containing short tandem repeat sequences (approximately 86-bp repeat) was isolated from a Xenopus laevis cDNA library. Southern blot and in situ hybridization analyses revealed that the repeat was highly dispersed in the genome and was present at approximately 1 million copies per haploid genome. We named this element Xstir (Xenopus short tandemly and invertedly repeating element) after its arrangement in the genome. The majority of the genomic Xstir sequences were digested to monomer and dimer sizes with several restriction enzymes. Their sequences were found to be highly homogeneous and organized into tandem arrays in the genome. Alignment analyses of several known sequences showed that some of the Xstir-like sequences were also organized into interspersed inverted repeats. The inverted repeats consisted of an inverted pair of two differently modified Xstirs separated by a short insert. In addition, these were framed by another novel inverted repeat (Xstir-TIR). The Xstir-TIR sequence was also found at the ends of tandem Xstir arrays. Furthermore, we found that Xstir-TIR was linked to a motif characterizing the T2 family which belonged to a vertebrate MITE (miniature inverted-repeat transposable element) family, suggesting the importance of Xstir-TIR for their amplification and transposition. The present study of 11 anuran and 2 urodele species revealed that Xstir or Xstir-like sequences were extensively amplified in the three Xenopus species. Genomic Xstir populations of X. borealis and X. laevis were mutually indistinguishable but significantly different from that of X. tropicalis. Received: 5 April 2000 / Accepted: 3 August 2000     

Molecular phylogeny of Omaliinae (Coleoptera: Staphylinidae) and its implications for evolution of atypically long elytra in rove beetles

Staphylinidae, or rove beetles, are a megadiverse family known for their typically very short elytra exposing most of the abdomen, but the putatively early-derived subfamily Omaliinae and its relatives have been known to include multiple taxa with unusually long elytra. The ancestral elytral length of the family and of this subfamily have long been debated. We present a phylogenetic analysis of Omaliinae based on partial mitochondrial COI (1488 bp), COII (366 bp), 12S rDNA (353 bp), nuclear 18S rDNA (1814 bp), 28S rDNA (876 bp) and CAD (869 bp) data. In all, 51 species in 31 genera and four outgroup species were included. The concatenated sequences were analysed by both parsimony- and model-based (Bayesian and maximum likelihood) methods. The subfamily Omaliinae was not supported as a monophyletic group. The model-based analyses (Bayesian and maximum likelihood trees) showed Empelinae nested within Omaliinae (excluding Corneolabiini), whereas parsimony analysis found all three putative ingroup subfamilies, Empelinae, Glypholomatinae and Microsilphinae, grouped within Omaliinae. Within the Omaliinae, the tribes Coryphiini and Eusphalerini were each supported as monophyletic, whereas Anthophagini and Omaliini were each nonmonophyletic. We hypothesize that there have been at least four independent origins of long elytra from short elytra in the omaliine lineage.     

An Improvement of the Westlake Symmetric Confidence Interval

A common statistical method for assessing bioequivalence of two formulations of a chemical substance is the symmetric confidence interval of WESTLAKE (1972). As mentioned by WEST -LAKE (1981) and SCHUIRMAN (1981) a more powerful method consists of two one-sided t-tests. An (1-α)-confidence interval consistent with the two one-sided t-tests procedure is given by [min(α, 0), max (0, b)] where [a, b] is the conventional (1–2α)-confidence interval of the t-test. This “central” confidence interval is always a strict subset of the symmetric confidence interval and thus has more power in proving bioequivalence. The central confidence interval has properties comparable with those of the conventional one-sided confidence intervals.     

Tables and Applications of the Bonferroni t-Statistics: A Revision of Dunn's Simultaneous t-Tests

Tables for Bonferroni-adjusted significance levels of Student's t are provided for r = 3(1)30(5)50 etc. and alphas of 0.05, 0.01 and 0.001. The tables are suggested for various applications, for example in replacing analysis of variance of k samples by r simultaneous t tests. Use of the tables is shown by numerical examples. The adjustment of alpha for improving the efficiency of testing is made by WILKINSON for orthogonal comparisons and by HOLM for nonorthogonal comparisons.     

How to Use the Two Sample t-Test

This work discusses how two sample t-tests behave when applied to data that may violate the classical statistical assumptions of independence, heteroscedasticity and Gaussianity. The usual two sample t-statistic based on a pooled variance estimate and the Welch-Aspin statistic are treated in detail. Practical “rules-of-thumb” are given along with their applications to various examples so that readers will easily be able to use such tests on their own data sets.     

Ancestral Population Sizes and Species Divergence Times in the Primate Lineage on the Basis of Intron and BAC End Sequences

The effective sizes of ancestral populations and species divergence times of six primate species (humans, chimpanzees, gorillas, orangutans, and representatives of Old World monkeys and New World monkeys) are estimated by applying the two-species maximum likelihood (ML) method to intron sequences of 20 different loci. Examination of rate heterogeneity of nucleotide substitutions and intragenic recombination identifies five outrageous loci (ODC1, GHR, HBE, INS, and HBG). The estimated ancestral polymorphism ranges from 0.21 to 0.96% at major divergences in primate evolution. One exceptionally low polymorphism occurs when African and Asian apes diverged. However, taking into consideration the possible short generation times in primate ancestors, it is concluded that the ancestral population size in the primate lineage was no smaller than that of extant humans. Furthermore, under the assumption of 6 million years (myr) divergence between humans and chimpanzees, the divergence time of humans from gorillas, orangutans, Old World monkeys, and New World monkeys is estimated as 7.2, 18, 34, and 65 myr ago, respectively, which are generally older than traditional estimates. Beside the intron sequences, three other data sets of orthologous sequences are used between the human and the chimpanzee comparison. The ML application to these data sets including 58,156 random BAC end sequences (BES) shows that the nucleotide substitution rate is as low as 0.6–0.8 × 10^–9 per site per year and the extent of ancestral polymorphism is 0.33–0.51%. With such a low substitution rate and short generation time, the relatively high extent of polymorphism suggests a fairly large effective population size in the ancestral lineage common to humans and chimpanzees.[Reviewing Editor: Dr. Magnus Nordborg]     

Phylogenetic relationships among diploid Aegilops species inferred from 5S rDNA units

Relationships among the currently recognized 11 diploid species within the genus Aegilops have been investigated. Sequence similarity analysis, based upon 363 sequenced 5S rDNA clones from 44 accessions plus 15 sequences retrieved from GenBank, depicted two unit classes labeled the long AE1 and short AE1. Several different analytical methods were applied to infer relationships within haplomes, between haplomes and among the species, including maximum parsimony and maximum likelihood analyses of consensus sequences, “total evidence” phylogeny analysis and “matrix representation with parsimony” analysis. None were able to depict suites of markers or unit classes that could discern among the seven haplomes as is observed among established haplomes in other genera within the tribe Triticeae; however, most species could be separated when displayed on gene trees. These results suggest that the haplomes currently recognized are so refined that they may be relegated as sub-haplomes or haplome variants. Amblyopyrum shares the same 5S rDNA unit classes with the diploid Aegilops species suggesting that it belongs within the latter. Comparisons of the Aegilops sequences with those of Triticum showed that the long AE1 unit class of Ae. tauschii shared the clade with the equivalent long D1 unit class, i.e., the putative D haplome donor, but the short AE1 unit class did not. The long AE1 unit class but not the short, of Ae. speltoides and Ae. searsii both share the clade with the previously identified long {S1 and long G1 unit classes meaning that both Aegilops species can be equally considered putative B haplome donors to tetraploid Triticum species. The semiconserved nature of the nontranscribed spacer in Aegilops and in Triticeae in general is discussed in view that it may have originated by processes of incomplete gene conversion or biased gene conversion or birth-and-death evolution.     

The discrimination of high-risk HPV types by in situ hybridization and the polymerase chain reaction

Summary The parameter Tm^t has been defined by non-isotopic in situ hybridization and describes the tissue melting temperature (Tm^t) of human papillomavirus (HPV) DNA sequences. In this study, multiple in situ hybridization signals for HPV types 16, 31 and 33 in individual archival biopsies hybridized with genomic probes are shown by polymerase chain reactions to be due to cross-hybridization of probe sequences to a single tissue target. Tm^t is independent of viral type but depends on the homology between probe and target when using nick-translated whole genomic probes. The difference between Tm and Tm^t is not due to the presence of viral capsid protein. Multiple HPV signals in archival material should not therefore be interpreted as indicative of multiple HPV infection unless adequate stringency conditions have been employed or they are present in morphologically distinct areas of the biopsy.Furthermore, extrapolation of calculated DNA homologies to non-isotopic in situ hybridization analysis may not be appropriate. A hybridization signal does not imply probe and target identity: this has implications for HPV typing in clinical material.     

Integral equation methods for computing likelihoods and their derivatives in the stochastic integrate-and-fire model

We recently introduced likelihood-based methods for fitting stochastic integrate-and-fire models to spike train data. The key component of this method involves the likelihood that the model will emit a spike at a given time t. Computing this likelihood is equivalent to computing a Markov first passage time density (the probability that the model voltage crosses threshold for the first time at time t). Here we detail an improved method for computing this likelihood, based on solving a certain integral equation. This integral equation method has several advantages over the techniques discussed in our previous work: in particular, the new method has fewer free parameters and is easily differentiable (for gradient computations). The new method is also easily adaptable for the case in which the model conductance, not just the input current, is time-varying. Finally, we describe how to incorporate large deviations approximations to very small likelihoods. Action Editor: Barry J. Richmond     

Asymptotic theory for analyzing dose-response survival data with application to the low-dose extrapolation problem

A model of the form P(t, d)=1−;exp{-(t)σ^K_i=0q_idⁱ}, q_i 0, is proposed for analyzing dose-response survival data with right censoring. The q_i's in the dose polynomial are estimated by maximizing the Cox partial likelihood, and given these estimates. Λ(t) is estimated nonparametrically by an estimator proposed by Breslow. Large-sample properties of these estimators are established. Estimates and related large-sample properties are provided for the “virtually safe dose” and other parameters for assessing low-dose carcinogenic risk as a function of age, using data from animal carcinogenesis experiments.     

Robust linear mixed models using the skew t distribution with application to schizophrenia data

We consider an extension of linear mixed models by assuming a multivariate skew t distribution for the random effects and a multivariate t distribution for the error terms. The proposed model provides flexibility in capturing the effects of skewness and heavy tails simultaneously among continuous longitudinal data. We present an efficient alternating expectation‐conditional maximization (AECM) algorithm for the computation of maximum likelihood estimates of parameters on the basis of two convenient hierarchical formulations. The techniques for the prediction of random effects and intermittent missing values under this model are also investigated. Our methodologies are illustrated through an application to schizophrenia data.     

The Estimation of a Multivariate Fitness Function from Several Samples Taken from a Population

The situation is considered where the multivariate distribution of certain variables X₁, X₂, …, X_p is changing with time in a population because natural selection related to the X's is taking place. It is assumed that random samples taken from the population at times t₁, t₂, …, t_s are available and it is desirable to estimate the fitness function w_t(x₁, x₂,…,x_p) which shows how the number of individuals with X_i = x_i, i = 1, 2, …, p at time t is related to the number of individuals with the same X values at time zero. Tests for population changes are discussed and indices of the selection on the population dispersion and the population mean are proposed. The situation with a multivariate normal distribution is considered as a special case. A maximum likelihood method that can be applied with any form of population distribution is proposed for estimating w_t. The methods discussed in the paper are illustrated with data on four dimensions of male Egyptian skulls covering a time span from about 4500 B.C. to about 300 A.D. In this case there seems to have been very little selection on the population dispersion but considerable selection on means.     

Improved LASSO priors for shrinkage quantitative trait loci mapping

Recently, the Bayesian least absolute shrinkage and selection operator (LASSO) has been successfully applied to multiple quantitative trait loci (QTL) mapping, which assigns the double-exponential prior and the Student’s t prior to QTL effect that lead to the shrinkage estimate of QTL effect. However, as reported by many researchers, the Bayesian LASSO usually cannot effectively shrink the effects of zero-effect QTL very close to zero. In this study, the double-exponential prior and Student’s t prior are modified so that the estimate of the effect for zero-effect QTL can be effectively shrunk toward zero. It is also found that the Student’s t prior is virtually the same as the Jeffreys’ prior, since both the shape and scale parameters of the scaled inverse Chi-square prior involved in the Student’s t prior are estimated very close to zero. Besides the two modified Bayesian Markov chain Monte Carlo (MCMC) algorithms, an expectation–maximization (EM) algorithm with use of the modified double-exponential prior is also adapted. The results shows that the three new methods perform similarly on true positive rate and false positive rate for QTL detection, and all of them outperform the Bayesian LASSO.     

Predicting sequence-dependent melting stability of short duplex DNA oligomers

Many important applications of DNA sequence-dependent hybridization reactions have recently emerged. This has sparked a renewed interest in analytical calculations of sequence-dependent melting stability of duplex DNA. In particular, for many applications it is often desirable to accurately predict the transition temperature, or t_m, of short duplex DNA oligomers (∼ 20 base pairs or less) from their sequence and concentration. The thermodynamic analytical method underlying these predictive calculations is based on the nearest-neighbor model. At least 11 sets of nearest-neighbor sequence-dependent thermodynamic parameters for DNA have been published. These sets are compared. Use of the nearest-neighbor sets in predicting t_m from the DNA sequence is demonstrated, and the ability of the nearest-neighbor parameters to provide accurate predictions of experimental t_m's of short duplex DNA oligomers is assessed. © 1998 John Wiley & Sons, Inc. Biopoly 44: 217–239, 1997     

Conformational analysis of polytripeptides (Gly-Pro-Ala)n, (Gly-Ala-Hyp)n,and (Gly-Ala-Ala)n in connection with the problem of collagen structure

Conformational analysis of triple helics of a type of collagen was performed with typical collagen tripeptide sequences based on Gly-Pro-Ala, Gly-Ala-Hyp, and Gly-Ala-Ala. During energy minimization, the possibility of continual deformation of the pyrrolidine cycle was taken into account in order to achieve better accuracy in the resulting structure. The (Gly-Pro-Ala)_n structure is almost isomorphic to the (Gly-Pro-Hyp)_n structure obtained in the previous work [Tumanyan, V. G. & Esipova, N.G. (1982) Biopolymers 21 , 475–497]. For a collagen-type structure, the optimal conformation of (Gly-Ala-Hyp)_n tends to have a decreased unit twist (t = 15°), although the energy advantage with respect to the conformation with t = 45° is not so significant. A similar situation is observed for (Gly-Ala-Ala)_n. In this case, the energy decrease during unwinding to t = 15° from t = 45° is quite small. The conformations of (Gly-Ala-Hyp)_n and (Gly-Ala-Ala)_n with t = 15° exhibit a similarity with a triple complex of polyproline II helices—a noncoiled coil such as (Gly-Pro-Hyp)_n and (Gly-Pro-Ala)_n. A similar structure may be postulated for subcomponent cq1 of the first component of a human complement containing substantial Gly-X-Pro and Gly-X-Y tripeptide derivatives in the primary structure (X, Y = any amino acid). The results suggest that the observed helical symmetry of collagen (t = 36°) is a consequence of superposition of diffraction patterns (for sufficiently long segments) from various helices (t varies from ～15° for Gly-X-Hyp and Gly-X-Y to ～56° for Gly-Pro-Ala). For short alternating segments, some unification of different helical structures is possible.