On an Unbiased Variance Estimator for the WILCOXON-MANN-WHITNEY-Statistic Based on Ranks

For some applications of the WILCOXON-MANN-WHITNEY-statistic its variance has to be estimated. So e.g. for the test of POTTHOFF (1963) to detect differences in medians of two symmetric distributions as well as for the computation of approximate, confidence bounds for the probability P(X₁ ≥ X₂), cf. GOVINDARAJULU (1968). In the present paper an easy to compute variance estimator is proposed which as only information uses the ranks of the data with the additional property that it is unbiased for the finite variance. Because of its invariance under any monotone transformation of the data its applicability is not confined to quantitative data. The estimator may be applied to ordinal data just as well. Some properties are discussed and a numerical example is given.     

Spherical Influenza Viruses Have a Fitness Advantage in Embryonated Eggs,while Filament-Producing Strains Are Selected In Vivo

Influenza viruses can take on two distinct morphologies: filamentous or spherical. While the functional significance of each virion type is unclear, filaments are generally observed in low-passage-number isolates, while an exclusively spherical morphology is seen in strains grown extensively in laboratory substrates. Previous studies have shown that filamentous morphology is lost upon passage in eggs. The fact that the filamentous morphology is maintained in nature but not in the laboratory suggests that filaments provide an advantage in the host that is not necessary for growth in laboratory substrates. To test this hypothesis and identify naturally occurring mutations that alter morphology, we examined the effect of serial adaptation in eggs, MDCK cells, and guinea pigs. Two filamentous strains, A/Netherlands/602/2009 (H1N1) and A/Georgia/M5081/2012 (H1N1), were passaged in eggs and MDCK cells. Conversely, the spherical laboratory strain A/Puerto Rico/8/1934 (H1N1) was passaged in guinea pigs. We found that although passage in eggs and MDCK cells can lead to a loss of filaments, an exclusively spherical morphology is not required for highly efficient growth in either substrate. We did, however, identify two point mutations in the matrix of egg passage 10 isolates that confer spherical morphology and increased growth in eggs. In contrast, serial passage in guinea pigs resulted in the selection of filament-forming variants. Sequencing revealed point mutations to the PR8 matrix that, when introduced individually, yielded filaments. These findings suggest a functional role for filaments in the infected host and expand the breadth of mutations known to affect influenza virus shape.     

The Hitchhiking Effect of a Strongly Selected Substitution in Male Germline on Neutral Polymorphism in a Monogamy Population

Comparative genomic studies suggest that a huge number of genes that show the strongest evidence for positive selection in human are testis- or sperm-specific genes, which are possibly due to germline selection. We propose a novel selection model in which the germlines of heterozygous males in a monogamous population are under natural selection. Under this model, we study the dynamics of a strongly selected substitution in the male germline and its hitch-hiking effect on the preexisting linked neutral polymorphism. We show that the expected heterozygosity at the neural locus is reduced by , where c is the recombination rate between selected and neutral locus, s is selective coefficient of advantageous allele, and N is diploid effective population size.     

Directional Variance Adjustment: Bias Reduction in Covariance Matrices Based on Factor Analysis with an Application to Portfolio Optimization

Robust and reliable covariance estimates play a decisive role in financial and many other applications. An important class of estimators is based on factor models. Here, we show by extensive Monte Carlo simulations that covariance matrices derived from the statistical Factor Analysis model exhibit a systematic error, which is similar to the well-known systematic error of the spectrum of the sample covariance matrix. Moreover, we introduce the Directional Variance Adjustment (DVA) algorithm, which diminishes the systematic error. In a thorough empirical study for the US, European, and Hong Kong stock market we show that our proposed method leads to improved portfolio allocation.     

Confidence Intervals on the Total Variance in an Unbalanced Two-fold Nested Design

Confidence intervals on the total variance in an unbalanced random two-fold nested design are constructed and compared. Computer simulation indicates the proposed intervals provide confidence coefficients that are generally close to the stated level.     

Estimation of Variance Components Based on a Diallel Model Involving Maternal and Maternal Interaction Effects

For a diallel model (TOPHAM, 1966) estimators of variance components are obtained by adopting the general approach outlined by SEELY (1969, 1970, 1971), SEELY and ZYSKIND (1971) and YUAN (1977) in the case of unbalanced data.     

Alternative Sigma Factor SigK Has a Role in Stress Tolerance of Group I Clostridium botulinum Strain ATCC 3502

The role of the alternative sigma factor SigK in cold and osmotic stress tolerance of Clostridium botulinum ATCC 3502 was demonstrated by induction of sigK after temperature downshift and exposure to hyperosmotic conditions and by impaired growth of the sigK mutants under the respective conditions.     

Chlamydomonas Inner-Arm Dynein Mutant, ida5, Has a Mutation in an Actin-encoding Gene

Chlamydomonas flagellar inner-arm dynein consists of seven subspecies (a–g), of which all but f contain actin as subunits. The mutant ida5 and a new strain, ida5-t, lack four subspecies (a, c, d, and e). These mutants were found to have mutations in the conventional actin gene, such that its product is totally lost; ida5 has a single-base deletion that results in a stop codon at a position about two-thirds from the 5′ end of the coding region, and ida5-t lacks a large portion of the entire actin gene. Two-dimensional gel electrophoresis patterns of the axonemes and inner-arm subspecies b and g of ida5 lacked the spot of actin (isoelectric point [pI] = ~5.3) but had two novel spots with pIs of ~5.6 and ~5.7 instead. Western blot with different kinds of anti-actin antibodies suggested that the proteins responsible for the two novel spots and conventional actin are different but share some antigenicity. Since Chlamydomonas has been shown to have only a single copy of the conventional actin gene, it is likely that the novel spots in ida5 and ida5-t originated from another gene(s) that codes for a novel actin-like protein(s) (NAP), which has hitherto been undetected in wildtype cells. These mutants retain the two inner-arm subspecies b and g, in addition to f, possibly because NAP can functionally substitute for the actin in these subspecies while they cannot in other subspecies. The net growth rate of ida5 and ida5-t cells did not differ from that of wild type, but the mating efficiency was greatly reduced. This defect was apparently caused by deficient growth of the fertilization tubule. These results suggest that NAP can carry out some, but not all, functions performed by conventional actin in the cytoplasm and raise the possibility that Chlamydomonas can live without ordinary actin.     

On the Effect of Unbalancedness and Heteroscedasticity on the ANOVA Estimator of Group Variance Component in One-Way Random Model

The expression for rth cumulant of ANOVA estimator of group variance component is derived in the One-way unbalanced random model under heteroscedasticity. The expression is used to study the effect of unbalancedness and heteroscedasticity on the mean and variance of the estimator, numerically. The computed results reveal that the unbalancedness and heteroscedasticity have a combined effect on the mean and variance of the estimator. For certain situations of unequal group sizes and error variances, the mean and variance of the estimator are increased and for certain other situations the values are decreased.     

Confidence Intervals and Tests of Hypotheses on Variance Components in an Unbalanced Two-fold Nested Design

Confidence intervals and tests of hypotheses on variance components are required in studies that employ a random effects design. The unbalanced random two-fold nested design is considered in this paper and confidence intervals are proposed for the variance components σ2/A and σ2/B. Computer simulation is used to show that even in very unbalanced designs, these intervals generally maintain the stated confidence coefficient. The hypothesis test for σ2/A based on the lower bound of the recommended confidence interval is shown to be better than previously proposed approximate tests.     

Multiplexing of ChIP-Seq Samples in an Optimized Experimental Condition Has Minimal Impact on Peak Detection

Multiplexing samples in sequencing experiments is a common approach to maximize information yield while minimizing cost. In most cases the number of samples that are multiplexed is determined by financial consideration or experimental convenience, with limited understanding on the effects on the experimental results. Here we set to examine the impact of multiplexing ChIP-seq experiments on the ability to identify a specific epigenetic modification. We performed peak detection analyses to determine the effects of multiplexing. These include false discovery rates, size, position and statistical significance of peak detection, and changes in gene annotation. We found that, for histone marker H3K4me3, one can multiplex up to 8 samples (7 IP + 1 input) at ~21 million single-end reads each and still detect over 90% of all peaks found when using a full lane for sample (~181 million reads). Furthermore, there are no variations introduced by indexing or lane batch effects and importantly there is no significant reduction in the number of genes with neighboring H3K4me3 peaks. We conclude that, for a well characterized antibody and, therefore, model IP condition, multiplexing 8 samples per lane is sufficient to capture most of the biological signal.     

Critical Mutation Rate Has an Exponential Dependence on Population Size in Haploid and Diploid Populations

Understanding the effect of population size on the key parameters of evolution is particularly important for populations nearing extinction. There are evolutionary pressures to evolve sequences that are both fit and robust. At high mutation rates, individuals with greater mutational robustness can outcompete those with higher fitness. This is survival-of-the-flattest, and has been observed in digital organisms, theoretically, in simulated RNA evolution, and in RNA viruses. We introduce an algorithmic method capable of determining the relationship between population size, the critical mutation rate at which individuals with greater robustness to mutation are favoured over individuals with greater fitness, and the error threshold. Verification for this method is provided against analytical models for the error threshold. We show that the critical mutation rate for increasing haploid population sizes can be approximated by an exponential function, with much lower mutation rates tolerated by small populations. This is in contrast to previous studies which identified that critical mutation rate was independent of population size. The algorithm is extended to diploid populations in a system modelled on the biological process of meiosis. The results confirm that the relationship remains exponential, but show that both the critical mutation rate and error threshold are lower for diploids, rather than higher as might have been expected. Analyzing the transition from critical mutation rate to error threshold provides an improved definition of critical mutation rate. Natural populations with their numbers in decline can be expected to lose genetic material in line with the exponential model, accelerating and potentially irreversibly advancing their decline, and this could potentially affect extinction, recovery and population management strategy. The effect of population size is particularly strong in small populations with 100 individuals or less; the exponential model has significant potential in aiding population management to prevent local (and global) extinction events.     

Effect of Sulfide on Nitrogen Fixation in a Stream Sediment-Water System

Nitrogen fixation (C₂H₂ reduction) in a sediment-water system was studied under anaerobic incubation conditions. Sodium sulfide at low concentrations stimulated activity, with a twofold increase in C₂H₄ production occurring in the presence of 8 μmol of S²⁻ per ml of stream water. Sodium sulfide at concentrations of 16 μmol of S²⁻ per ml or greater inhibited nitrogen fixation, with 64 μmol of S²⁻ per ml being completely inhibitory. Sulfide at levels of 16 μmol/ml or above inhibited CO₂ production, and the degree of inhibition increased with increasing concentration of sulfide. Titanium (III) citrate (used to modify Eh levels) stimulated both nitrogen fixation and CO₂ production, but could not duplicate, at any concentration tested, the twofold increase in nitrogen fixation caused by 8 μmol of S²⁻ per ml. Sulfide additions caused pH changes in the sediment, and when the sediment was adjusted and maintained at pH 7.0 all concentrations of sulfide inhibited nitrogen fixation activity. From considerations of the redox equilibria of H₂, H₂S, and other sulfur species at various pH values, it appeared that H₂S was the toxic entity and that HS⁻ was less toxic. The observed stimulation of activity was apparently due to a pH change coupled with the concurrent production of HS⁻ from H₂S.     

Recombination Accelerates Adaptation on a Large-Scale Empirical Fitness Landscape in HIV-1

Recombination has the potential to facilitate adaptation. In spite of the substantial body of theory on the impact of recombination on the evolutionary dynamics of adapting populations, empirical evidence to test these theories is still scarce. We examined the effect of recombination on adaptation on a large-scale empirical fitness landscape in HIV-1 based on in vitro fitness measurements. Our results indicate that recombination substantially increases the rate of adaptation under a wide range of parameter values for population size, mutation rate and recombination rate. The accelerating effect of recombination is stronger for intermediate mutation rates but increases in a monotonic way with the recombination rates and population sizes that we examined. We also found that both fitness effects of individual mutations and epistatic fitness interactions cause recombination to accelerate adaptation. The estimated epistasis in the adapting populations is significantly negative. Our results highlight the importance of recombination in the evolution of HIV-I.     

Broadly Neutralizing Antibodies Developed by an HIV-Positive Elite Neutralizer Exact a Replication Fitness Cost on the Contemporaneous Virus

Approximately 1% of those infected with HIV-1 develop broad and potent serum cross-neutralizing antibody activities. It is unknown whether or not the development of such immune responses affects the replication of the contemporaneous autologous virus. Here, we defined a pathway of autologous viral escape from contemporaneous potent and broad serum neutralizing antibodies developed by an elite HIV-1-positive (HIV-1⁺) neutralizer. These antibodies potently neutralize diverse isolates from different clades and target primarily the CD4-binding site (CD4-BS) of the viral envelope glycoprotein. Viral escape required mutations in the viral envelope glycoprotein which limited the accessibility of the CD4-binding site to the autologous broadly neutralizing anti-CD4-BS antibodies but which allowed the virus to infect cells by utilizing CD4 receptors on their surface. The acquisition of neutralization resistance, however, resulted in reduced cell entry potential and slower viral replication kinetics. Our results indicate that in vivo escape from autologous broadly neutralizing antibodies exacts fitness costs to HIV-1.