Arnold Janssen

Acquisition of 1,000 eubacterial genes physiologically transformed a methanogen at the origin of Haloarchaea

Archaebacterial halophiles (Haloarchaea) are oxygen-respiring heterotrophs that derive from methanogens—strictly anaerobic, hydrogen-dependent autotrophs. Haloarchaeal genomes are known to have acquired, via lateral gene transfer (LGT), several genes from eubacteria, but it is yet unknown how many genes the Haloarchaea acquired in total and, more importantly, whether independent haloarchaeal lineages acquired their genes in parallel, or as a single acquisition at the origin of the group. Here we have studied 10 haloarchaeal and 1,143 reference genomes and have identified 1,089 haloarchaeal gene families that were acquired by a methanogenic recipient from eubacteria. The data suggest that these genes were acquired in the haloarchaeal common ancestor, not in parallel in independent haloarchaeal lineages, nor in the common ancestor of haloarchaeans and methanosarcinales. The 1,089 acquisitions include genes for catabolic carbon metabolism, membrane transporters, menaquinone biosynthesis, and complexes I–IV of the eubacterial respiratory chain that functions in the haloarchaeal membrane consisting of diphytanyl isoprene ether lipids. LGT on a massive scale transformed a strictly anaerobic, chemolithoautotrophic methanogen into the heterotrophic, oxygen-respiring, and bacteriorhodopsin-photosynthetic haloarchaeal common ancestor.

Origins of major archaeal clades correspond to gene acquisitions from bacteria.

The mechanisms that underlie the origin of major prokaryotic groups are poorly understood. In principle, the origin of both species and higher taxa among prokaryotes should entail similar mechanisms—ecological interactions with the environment paired with natural genetic variation involving lineage-specific gene innovations and lineage-specific gene acquisitions. To investigate the origin of higher taxa in archaea, we have determined gene distributions and gene phylogenies for the 267,568 protein-coding genes of 134 sequenced archaeal genomes in the context of their homologues from 1,847 reference bacterial genomes. Archaeal-specific gene families define 13 traditionally recognized archaeal higher taxa in our sample. Here we report that the origins of these 13 groups unexpectedly correspond to 2,264 group-specific gene acquisitions from bacteria. Interdomain gene transfer is highly asymmetric, transfers from bacteria to archaea are more than fivefold more frequent than vice versa. Gene transfers identified at major evolutionary transitions among prokaryotes specifically implicate gene acquisitions for metabolic functions from bacteria as key innovations in the origin of higher archaeal taxa.

Studentized permutation tests for non-i.i.d. hypotheses and the generalized Behrens-Fisher problem

It is shown that permutation tests based on studentized statistics are asymptotically exact of size [alpha] also under certain extended non-i.i.d. null hypotheses. To demonstrate the principle the results are applied to the generalized two-sample Behrens-Fisher problem for testing equality of the means under general non-parametric heterogeneous error distributions. Within this setting we propose a permutation version of the Welch test which is an extension of Pitmans two-sample permutation test. These results are special cases of a conditional central limit theorem for studentized permutation statistics which also applies to asymptotic power functions.

Testing nonparametric statistical functionals with applications to rank tests

Abstract The present paper discusses how nonparametric tests can be deduced from statistical functionals. Efficient and asymptotically most powerful maximin tests are derived. Their power function is calculated under implicit alternatives given by the functional for one – and two – sample testing problems. It is shown that the asymptotic power function does not depend on the special implicit direction of the alternatives but only on quantities of the functional. The present approach offers a nonparametric principle how to construct common rank tests as the Wilcoxon test, the log rank test, and the median test from special two-sample functionals. In addition it is shown that studentized permutation tests yield asymptotically valid tests for certain extended null hypotheses given by functionals which are strictly larger than the common i.i.d. null hypothesis. As example tests concerning the von Mises functional and the Wilcoxon two-sample test are treated.

A Monte Carlo comparison of studentized bootstrap and permutation tests for heteroscedastic two-sample problems

The present Monte Carlo study compares bootstrap and permutation tests for semiparametric heteroscedastic two-sample testing problems of Behrens-Fisher type. The underlying functionals to be tested are (a) the difference of the means and (b) the Wilcoxon functionalP(Y < X) which is invariant under strictly increasing transformations. The consideration leads to semiparametric modifications of Welch type tests for the Behrens-Fisher model and an extended two-sample Wilcoxon test which also works under some null hypothesis with non-exchangeable distributions. The present Monte Carlo study confirms the high quality of studentized permutation tests at finite sample size. They are typically better than tests with asymptotic critical values and for many situations and they are also better than two-sample bootstrap tests when their type I error probabilities are compared.

Principal component decomposition of non-parametric tests

SummaryLet ϕ denote an arbitrary non-parametric unbiased test for a Gaussian shift given by an infinite dimensional parameter space. Then it is shown that the curvature of its power function has a principal component decomposition based on a Hilbert-Schmidt operator. Thus every test has reasonable curvature only for a finite number of orthogonal directions of alternatives. As application the two-sided Kolmogorov-Smirnov goodnessof-fit test is treated. We obtain lower bounds for their local asymptotic relative efficiency. They converge to one as α↓0 for the directionh0(u)=sign(2u−1) of the gradient of the median test. These results are analogous to earlier results of Hájek and Šidák for one-sided Kolmogorov-Smirnov tests.

Infinitely divisible statistical experiments

I. Limits of Triangular Arrays of Experiments.- 1. Basic Concepts.- 2. Gaussian Experiments.- 3. Introduction to Poisson Experiments.- 4. Convergence of Poisson Experiments.- 5. Convergence of Triangular Arrays.- 6. Identification of Limit Experiments.- II. The Levy-Khintchine Formula for Infinitely Divisible Experiments.- 7. Preliminaries.- 8. Infinitely Divisible Probability Measures.- 9. The Levy-Khintchine Formula for Standard Measures.- 10. The Levy-Khintchine Formula for Arbitrary Regular Infinitely Divisible Statistical Experiments.- III. Representation of Poisson Experiments.- 11. Generalized Poisson Processes.- 12. Standard Poisson Experiments.- IV. Statistical Experiments with Independent Increments.- 13. Preliminaries.- 14. Experiments with Independent Increments.- 15. Existence and Construction of Experiments with Independent Increments.- 16. Infinitely Divisible Experiments with Independent Increments.- 17. Weak Convergence of Triangular Arrays to Experiments with Independent Increments.- 18. The Likelihood Process.- 19. Application to Densities with Jumps.- List of Symbols.- Author Index.

On statistical information of extreme order statistics, local extreme value alternatives, and poisson point processes

The aim of the present paper is to clarify the role of extreme order statistics in general statistical models. This is done within the general setup of statistical experiments in LeCams sense. Under the assumption of monotone likelihood ratios, we prove that a sequence of experiments is asymptotically Gaussian if, and only if, a fixed number of extremes asymptotically does not contain any information. In other words: A fixed number of extremes asymptotically contains information iff the Poisson part of the limit experiment is non-trivial. Suggested by this result, we propose a new extreme value model given by local alternatives. The local structure is described by introducing the space of extreme value tangents. It turns out that under local alternatives a new class of extreme value distributions appears as limit distributions. Moreover, explicit representations of the Poisson limit experiments via Poisson point processes are found. As a concrete example nonparametric tests for Frechet type distributions against stochastically larger alternatives are treated. We find asymptotically optimal tests within certain threshold models.

Non-standard rank tests

Locally most powerful rank tests finite sample results asymptotic results for locally most powerful rank tests asymptotic results for rank tests under alternatives tests based on minimum ranks parametric results for almost regular models semiparametric models and Monte Carlo results.

Brownian Type Boundary Crossing Probabilities for Piecewise Linear Boundary Functions

Abstract The present paper offers exact boundary crossing probabilities for the Brownian motion and the Brownian bridge when the boundary function is piecewise linear. They are mostly given for one-sided bounds. The probabilities are expressed by multivariate normal distributions given by a Sylvester type formula. Some applications are sketched in statistics for Kolmogorov–Smirnov type test statistics also when ties of the data are present. We offer error bounds for the crossing probabilities when the boundary function is approximated by another one.