Error estimation and global fitting in transverse-relaxation dispersion experiments to determine chemical-exchange parameters

Off-resonance effects can introduce significant systematic errors in R₂ measurements in constant-time Carr-Purcell-Meiboom-Gill (CPMG) transverse relaxation dispersion experiments. For an off-resonance chemical shift of 500 Hz, ¹⁵N relaxation dispersion profiles obtained from experiment and computer simulation indicated a systematic error of ca. 3%. This error is three- to five-fold larger than the random error in R₂ caused by noise. Good estimates of total R₂ uncertainty are critical in order to obtain accurate estimates in optimized chemical exchange parameters and their uncertainties derived from χ² minimization of a target function. Here, we present a simple empirical approach that provides a good estimate of the total error (systematic + random) in ¹⁵N R₂ values measured for the HIV protease. The advantage of this empirical error estimate is that it is applicable even when some of the factors that contribute to the off-resonance error are not known. These errors are incorporated into a χ² minimization protocol, in which the Carver–Richards equation is used fit the observed R₂ dispersion profiles, that yields optimized chemical exchange parameters and their confidence limits. Optimized parameters are also derived, using the same protein sample and data-fitting protocol, from ¹H R₂ measurements in which systematic errors are negligible. Although ¹H and ¹⁵N relaxation profiles of individual residues were well fit, the optimized exchange parameters had large uncertainties (confidence limits). In contrast, when a single pair of exchange parameters (the exchange lifetime, τ_ex, and the fractional population, p_a), were constrained to globally fit all R₂ profiles for residues in the dimer interface of the protein, confidence limits were less than 8% for all optimized exchange parameters. In addition, F-tests showed that quality of the fits obtained using τ_ex, p_a as global parameters were not improved when these parameters were free to fit the R₂ profiles of individual residues. Finally, nearly the same optimized global τ_ex, p_a values were obtained, when the ¹H and ¹⁵N data sets for residues in the dimer interface, were fit independently; the difference in optimized global parameters, ca. 10%, was of marginal significance according to the F-test.     

The use of jackknifing for the evaluation of geographic profiling reliability

The use of geographic profiling (GP), based on “Rossmo's formula”, a technique derived from criminology, has been previously proven to be effective in assessing the origin of invading species. The application on Caulerpa taxifolia showed the most probable center of spread of the invasion. This article discusses a method of assessing the degree of robustness of the results obtained with Rossmo's method.To provide an evaluation of the reliability of geographic profiling results we used the jackknife technique, randomly eliminating part of the data set for a given number of replicates (500) in order to analyze the obtained result for each replicate. In GP the results are a series of images with geoprofiling prioritization, each produced with one of the replicates. These images can be summarized in three different ways: (1) OR, depicting all the high probability pixels from the series of replicates; (2) AND, depicting only those high probability pixels present in every replicate; and (3) MEAN, depicting the mean color value for each pixel calculated from all the replicates. We show that jackknifing can be a useful method to increase robustness of GP analysis in criminology, epidemiology and biological invasions. Summarizing jackknifing results with the OR logical operator yields the highest sensitivity and worst specificity, while the use of the AND operator increases specificity but reduces sensitivity. Using the mean of the pixel values maintains the visualization of the areas of highest priority (specificity), while also showing the surrounding area with varying colors, analogous to confidence limits.     

Dynamic light scattering studies of internal motions in DNA. II. Clean viral DNAs

Internal Brownian motions of clean ?29 and λ-DNAs have been studied using photon-correlation techniques at both visible (λ₀ = 632.8 nm) and uv (λ₀ = 363.8 nm) wavelengths. The present dynamic light scattering data, which extend to K² = 19 × 10¹⁰ cm^?2, can in every case be satisfactorily simulated by a Rouse-Zimm model polymer with an appropriate choice of the three model parameters. The effects of pH, salt concentration, single-strand breaks, and molecular weight on those model parameters have also been investigated. Intact clean DNAs exhibit surprisingly little variation with pH from 7.85 to 10.25, with salt concentration from 0.01 NaCl to 5.4M NH₄Cl, or with molecular weight or GC content. The single-strand breaks have no effect at pH 9.46, but produce dramatic changes in the model parameters at pH 10.0 and 10.25, indicating the introduction of titratable joints at those pHs. The failure of either single-strand breaks or a large change in GC content to alter the model parameters in the neutral pH range is a strong indication that local denaturation is not required for those flexions and torsions that dominate the relaxation of fluctuations in the scattered light. The Langevin relaxation time for the slowest internal mode of a particular Rouse-Zimm model derived from the dynamic light scattering data is compared with pertinent literature data extrapolated to the same molecular weight. The present algorithm for determining model parameters from the light-scattering D_app vs K² curve actually yields a Langevin time in fairly good agreement with the literature value. For unknown reasons the light-scattering D₀ values generally exceed those obtained from the molecular weight and sedimentation coefficient by about 20%.     

Frigatebirds, Tropicbirds, and Ciconiida: Excesses of Confidence Probability

Because it is based on a significance test that takes the shape of the tree as given, the Rzhetsky/Nei Confidence Probability (CP) can attribute high "confidence" to groups with little or even literally no support. CP further overestimates confidence in that it takes no account of reliability of alignment, and it shows instability in that drastic changes in results can be produced by small changes in data. Instability can arise when alignment is uncertain, since different alignment strategies can lead to slightly different matrices. Parsimony jackknifing offers a more reliable and stable way of assessing support. To take ambiguities of alignment into account with parsimony jackknifing, we suggest "consensus" and "average" methods of summarizing jackknife results from several alignments. Reanalyzing 12S and 16S rRNA data on pelecaniform birds, we find that CP has overestimated support for the Ciconiida, for placing frigatebirds with condors, and for placing tropicbirds with cormorants.     

An expanded plastid DNA phylogeny of Orchidaceae and analysis of jackknife branch support strategy

An expanded plastid DNA phylogeny for Orchidaceae was generated from sequences of rbcL and matK for representatives of all five subfamilies. The data were analyzed using equally weighted parsimony, and branch support was assessed with jackknifing. The analysis supports recognition of five subfamilies with the following relationships: (Apostasioideae (Vanilloideae (Cypripedioideae (Orchidoideae (Epidendroideae))))). Support for many tribal-level groups within Epidendroideae is evident, but relationships among these groups remain uncertain, probably due to a rapid radiation in the subfamily that resulted in short branches along the spine of the tree. A series of experiments examined jackknife parameters and strategies to determine a reasonable balance between computational effort and results. We found that support values plateau rapidly with increased search effort. Tree bisection-reconnection swapping in a single search replicate per jackknife replicate and saving only two trees resulted in values that were close to those obtained in the most extensive searches. Although this approach uses considerably more computational effort than less extensive (or no) swapping, the results were also distinctly better. The effect of saving a maximal number of trees in each jackknife replicate can also be pronounced and is important for representing support accurately.     

Influence of pH on Terminal Carbon Metabolism in Anoxic Sediments from a Mildly Acidic Lake

The carbon and electron flow pathways and the bacterial populations responsible for transformation of H₂-CO₂, formate, methanol, methylamine, acetate, glycine, ethanol, and lactate were examined in sediments collected from Knaack Lake, Wis. The sediments were 60% organic matter (pH 6.2) and did not display detectable sulfate-reducing activity, but they contained the following average concentration (in micromoles per liter of sediment) of metabolites and end products: sulfide, 10; methane, 1,540; CO₂, 3,950; formate, 25; acetate, 157; ethanol, 174; and lactate, 138. Methane was produced predominately from acetate, and only 4% of the total CH₄ was derived from CO₂. Methanogenesis was limited by low environmental temperature and sulfide levels and more importantly by low pH. Increasing in vitro pH to neutral values enhanced total methane production rates and the percentage of CO₂ transformed to methane but did not alter the amount of ¹⁴CO₂ produced from [2-¹⁴C]acetate (~24%). Analysis of both carbon transformation parameters with ¹⁴C-labeled tracers and bacterial trophic group enumerations indicated that methanogenesis from acetate and both heterolactic- and acetic acid-producing fermentations were important to the anaerobic digestion process.     

Stimulation of metamorphosis in Hydractinia echinata involves generation of lysophosphatidylcholine

Summary Whilst the significance of the phosphoinositide cycle in the activation of developmental events by extra-cellular signals is well established, the involvement of the phosphatidylcholine (PC) cycle is a matter just emerging. In the present study, the metabolism of phosphatidylcholine in early metamorphosis of Hydractinia echinata (Coelenterata; Hydrozoa) was investigated by incubation of planula larvae with ³H-choline, extraction of the metabolites and isolation of the metabolites by thin-layer chromatography (TLC). Phosphatidylcholine (PC), lysophosphatidylcholine (LPC), acetylcholine and glycerophosphocholine were the labelled metabolites. Induction of metamorphosis did not stimulate an increased incorporation of choline into PC. In larvae preincubated with ³H-choline to a steady state level of incorporation, a significant transient elevation of the radioactive label in LPC was observed 90 min after addition of metamorphosis stimulating agents. LPC probably derived from PC by the action of a phospholipase A₂ (PLA₂). LPCs from bovine and soybean origin as well as isolated larval LPC did not influence metamorphosis. PLA₂ from bee venom promoted Cs⁺-induced metamorphosis but did not influence phorbol ester-induced metamorphosis. The data suggest that a PLA₂ is activated during metamorphosis. This PLA₂ activation does not occur in those putative receptor cells which receive the primary external inducing stimulus but in the many larval cells which resume proliferation or differentiation in response to a second, internally propagated signal. Offprint requests to: T. Leitz     

Inhibition of K+-sensitive p-nitrophenylphosphatase activity on rhesus-positive red cells after incubation with IgG-anti-rhesus-D

The incubation of ghosts derived from human Rhesus-positive red cells with IgG-anti-Rhesus-D inhibited the K⁺-sensitive p-nitrophenylphosphatase activity. This enzyme has a partial function in the (Na⁺ + K⁺)-ATPase system related to the phosphorylation step, which is important for active potassium transport through the red cell membrane. The specificity of the impairment by the antigen-antibody reaction in the Rhesus-D system was proved by the following controls. Ghosts obtained from Rhesus-negative red cells incubated by IgG-anti-Rhesus-D and those of Rhesus-positive red cells treated with non-immune serum did not show any reduction of the K⁺-p-nitrophenylphosphatase activity. The ghost preparation with lanthanum carried out after hypotonic hemolysis of the washed red cells in 2 mM LaCl₃ at pH 6 was the most suitable procedure to explore this topic in comparison to other techniques for preparing ghosts of red cells.     

Development of a diatom-based transfer function for lakes and streams severely impacted by secondary salinity in the south-west region of Western Australia

The association of diatom assemblages to salinity was studied in 95 lakes and streams ranging from freshwater to hypersaline in the south-west of Western Australia. The relationship between environmental variables and species composition was explored using canonical correspondence analysis (CCA) and partial CCA. Salinity was shown to account for a significant and independent amount of variation in the diatom data, enabling a transfer function to be developed based on the final dataset, which consisted of 89 sites and 150 diatom taxa. The most successful model was derived using tolerance-downweighted weighted averaging. Summary statistics showed that the transfer function performed very well with a high coefficient of determination and low prediction errors that remained high after the cross-validation method of jackknifing (r _apparent² = 0.97 and r _jackknifed² = 0.89). This suggests that salinity can be accurately predicted using relative abundances of diatoms, and the model can now be applied to paleolimnological reconstructions. However, the transfer function also provides the basis for use in future biomonitoring studies to detect increases in salinity for lakes and streams most at risk, as well as to evaluate the success of remediation measures implemented to secondary salinised systems. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users. Guest Editors: J. John & B. Timms Salt Lake Research: Biodiversity and Conservation—Selected papers from the 9th Conference of the International Society for Salt Lake Research     

Limiting the sedimentation coefficient for sedimentation velocity data analysis: partial boundary modeling and g(s) approaches revisited

Brown and coworkers (Eur. Biophys. J. 38 (2009) 1079–1099) introduced partial boundary modeling (PBM) to simplify sedimentation velocity data analysis by excluding species outside the range of interest (e.g., aggregates, impurities) via restricting the sedimentation coefficient range being fitted. They strongly criticized the alternate approach of fitting g(s^∗) distributions using similar range limits, arguing that (i) it produces “nonoptimal fits in the original data space” and (ii) the g(s^∗) data transformations lead to gross underestimates of the parameter confidence intervals. It is shown here that neither of those criticisms is valid. These two approaches are not truly fitting the same data or in equivalent ways; thus, they should not actually give the same best-fit parameters. The confidence limits for g(s^∗) fits derived using F statistics, bootstrap, or a new Monte Carlo algorithm are in good agreement and show no evidence for significant statistical distortion. Here 15 g(s^∗) measurements on monoclonal antibody samples gave monomer mass estimates with experimental standard deviations of less than 1%, close to the confidence limit estimates. Tests on both real and simulated data help to clarify the strengths and drawbacks of both approaches. New algorithms for computing g(s^∗) and a scan-differencing approach for PBM are introduced.     

Cytophotometric DNA determinations and autoradiographic studies in salivary gland nuclei from larvae with different karyotypes in Drosophila melanogaster

Cytophotometric DNA determinations in Feulgen stained mitotic diploid chromosome sets of neuroblasts from larvae of Drosophila melanogaster stocks, which possess different karyotypes, show significant differences between the 4C values, caused by an additional or deficient X- and Y-chromosome depending on the karyotype. The ranges of polytenic DNA size classes are theoretically expected to be doublings of the corresponding 4C mean value of each karyotype. The extinction integral data of nuclei with completely duplicated 4C quantities exclusively fall into the range of the expected size classes. Not all data falling into the range of a size class necessarily originate from duplicated nuclei, because the limits of the DNA size classes cannot be determined by measurements, but must be estimated from the confidence limits of the corresponding 4C mean value. The validity of the mitotic 4C values of the karyotypes X/X and X/Y is tested using data from non-labeled interphase nuclei, where extinction integral data accumulate in two groups. The larger values (= G₂-nuclei) confirm the 4C values of mitotic chromosome sets, and the lower values (= G₁-nuclei) are just half of these. Extinction integrals from individual, ³H-thymidine non-incorporating polytene salivary gland nuclei accumulate in distinct, non-overlapping groups which are always complete doublings of the preceding smaller group. In each karyotype, the most frequent data of each group are in accord with the 4C doublings. The data from labeled nuclei alternate with those from unlabeled nuclei. The measured DNA values of individual polytene nuclei that did not incorporate any ³H-thymidine, demonstrate that all chromosomal DNA replicates completely during polytenization of the chromosomes in the larval salivary gland nuclei of Drosophila melanogaster. Specifically, this would mean that the heterochromatic Y-chromosome replicates as well as the partially heterochromatic X-chromosome along with the autosomes. There is no indication of underreplicating heterochromatin.     

Effects of 2‐phenoxyethanol anaesthesia on juvenile meagre (Argyrosomus regius)

This study was performed to evaluate the effective concentration of the anaesthetic 2‐phenoxyethanol (2‐PE) on juvenile (1.3 ± 0.03 g) meagre (Argyrosomus regius, Asso, 1801) and establish the LC₅₀ (through a series of exposure concentrations) and LT₅₀ of 2‐PE at 20 ± 0.5°C, salinity 38 g × L^?1, pH 8.2–8.4 and dissolved oxygen >7 mg × L^?1. The induction time decreased and the recovery time increased with increasing concentrations. Conflicting results were found only in recovery time and there were no significant differences among the recovery times from all concentrations. The most suitable concentration of 2‐PE was 0.3 ml × L^?1 for about or over 15 min exposure time. The LC₅₀ and LT₅₀ for the 3–60 min exposure periods were estimated for juvenile meagre. The toxic effect of 2‐PE on survival rates of A. regius juveniles increased depending on the exposure period. In addition, 2‐phenoxyethanol LT₅₀ (median survival time) values, slope function (S) and lower and upper 95% confidence limits were estimated.     

Iron limitation of phytoplankton in an urbanized vs. forested southeastern U.S. salt marsh estuary

Over the last two decades, escalating rates of coastal development have altered macro- and micronutrient loading patterns to many southeastern U.S. estuaries. This study addresses a potential consequence of urbanization-associated coastal deforestation that may have important implications for estuarine ecosystem productivity: a reduction in bioavailable Fe. We compared the potential for Fe limitation at representative sites in two neighboring South Carolina salt marsh estuaries, one (“Parsonage Creek” site in Murrells Inlet estuary) impacted by urbanization-associated clear-cutting, and the other (“Oyster Landing” site in North Inlet estuary) undeveloped and surrounded by forests. The urbanized estuarine site was marked by lower dissolved Fe concentrations compared to the forested estuarine site. In bioassay experiments conducted from 1996 to 1999, the addition of chelated Fe to natural phytoplankton populations stimulated chlorophyll a concentrations in water from Parsonage Creek on 6 of 11 sampling dates. Chlorophyll responses in Oyster Landing water also were observed on two of those sampling times, dates that followed periods of relatively low rainfall. In one experiment, the addition of Fe+NO₃⁻ to Parsonage Creek water led to significantly higher chlorophyll concentrations than when NO₃⁻ was added alone, but Fe+NH₄⁺ addition did not result in higher chlorophyll than NH₄⁺ addition alone. It was hypothesized that the difference in NO₃⁻ and NH₄⁺ responses was related to a greater tendency towards Si depletion in Fe-stressed NO₃⁻-grown samples, or alternatively, to the higher Fe requirement for NO₃⁻ assimilation relative to that needed for NH₄⁺ assimilation. In bioassay experiments using Fe-deplete semi-continuous cultures of Synechococcus WH8101, Fe addition did not affect the net growth rate of cultures transferred to water from either estuary, but increased the chlorophyll a content of cells transferred to Parsonage Creek water. Finally, photosynthesis vs. irradiance parameters (α, P_max) obtained from Oyster Landing samples (<2 μm size fraction) were similar to those measured in Fe-replete Synechococcus continuous cultures, while the same parameters derived from Parsonage Creek samples were much lower and comparable to those from Fe-deplete cultures. The results indicate that phytoplankton population growth from high salinity salt marsh estuaries can be Fe-limited. Also, the potential for Fe limitation was more prevalent in a urbanized deforested estuary than in an undeveloped forested estuary, consistent with the hypothesis that organically bound Fe from coastal forests plays an important role in supplying Fe for the growth of estuarine phytoplankton.     

Concurrent validity of the Microsoft Kinect for assessment of spatiotemporal gait variables

Spatiotemporal characteristics of gait such as step time and length are often associated with overall physical function in clinical populations, but can be difficult, time consuming and obtrusive to measure. This study assessed the concurrent validity of overground walking spatiotemporal data recorded using a criterion reference – a marker-based three-dimensional motion analysis (3DMA) system – and a low-cost, markerless alternative, the automated skeleton tracking output from the Microsoft Kinect™ (Kinect). Twenty-one healthy adults performed normal walking trials while being monitored using both systems. The outcome measures of gait speed, step length and time, stride length and time and peak foot swing velocity were derived using supervised automated analysis. To assess the agreement between the Kinect and 3DMA devices, Bland–Altman 95% bias and limits of agreement, percentage error, relative agreement (Pearson's correlation coefficients: r) overall agreement (concordance correlation coefficients: r_c) and landmark location linearity as a function of distance from the sensor were determined. Gait speed, step length and stride length from the two devices possessed excellent agreement (r and r_c values >0.90). Foot swing velocity possessed excellent relative (r=0.93) but only modest overall (r_c=0.54) agreement. Step time (r=0.82 and r_c=0.23) and stride time (r=0.69 and r_c=0.14) possessed excellent and modest relative agreement respectively but poor overall agreement. Landmark location linearity was excellent (R²=0.991). This widely available, low-cost and portable system could provide clinicians with significant advantages for assessing some spatiotemporal gait parameters. However, caution must be taken when choosing outcome variables as some commonly reported variables cannot be accurately measured.     

Xylem-solute technique to measure N2 fixation by Phaseolus vulgaris L.: Calibration and sources of error

Utilising the ¹⁵N dilution technique the relationship between the proportion of N derived from N₂ fixation and relative abundance of ureides in xylem sap was evaluated for Phaseolus vulgaris L. cv. Mokcham during vegetative and reproductive development. In order to establish calibration curves for time integrated estimates of N₂ fixation, plants were raised in sand culture during the dry season in northern Thailand and continuously supplied with a N-free nutrient solution or the same solution amended with 0, 3, 6 or 9 mol m^–3 nitrate. Large changes in plant dependence on N₂ fixation were concomitantly reflected by corresponding alterations in N solutes in xylem sap. Regression analyses of the data suggested high correlations between relative ureide content and N₂ fixation, but different slopes and line intercepts indicated the requirement for the use of calibration curves established for different phases of the development of the plant. Largest age related differences were noted between vegetative and reproductive development. Judging from 95% confidence limits, utilisation of appropriate calibrations can reduce errors of the technique to close to ±5%.A second experiment, involving similarly cultivated plants exposed to different sources of mineral N, indicated an effect of ammonium on xylem sap composition. This implies that calibrations, in which N₂ fixation is regulated only by applications of various concentrations of nitrate, may lead to errors in situations where a major proportion of the plant available soil nitrogen fraction is present in the form of ammonium.     

Determination of the pseudoephedrine content in pharmaceutical formulations and in biological fluids using a microbore HPLC system interfaced to a microfluidic chemiluminescence detector

A novel automated precolumn derivatization followed by separation using liquid chromatography for the determination of pseudoephedrine (PSE) by a microfluidic chemiluminescence detector has been developed. An on‐line derivatization procedure was utilized by converting PSE into a highly light emitting species in a Ru(bipy)₃²⁺‐peroxydisulphate chemiluminescence (CL) system by derivatizing it with a 1.0 M formaldehyde solution. The derivatized analyte was directly injected into a microbore high‐performance liquid chromatography (HPLC) system coupled to an on‐chip chemiluminescence detector. The newly developed highly selective, sensitive and fast HPLC‐CL method was validated and successfully applied for the analysis of PSE in pharmaceutical formulations and a human urine sample. The selectivity of the method is not only due to the HPLC separation but is also due to the highly selective detection principle of the Ru(bipy)₃²⁺‐peroxydisulphate CL system used. There was no interference observed from the common preservatives and excipients used in pharmaceutical preparations, which did not show any significant CL signal. The retention time of PSE was less than 3 min, and the detection limits and quantification limits were found to be 5.7 and 26.0 µg L^–1, respectively. Copyright © 2015 John Wiley & Sons, Ltd.     

Nitrogen addition alters mineralization dynamics of 13C‐depleted leaf and twig litter and reduces leaching of older DOC from mineral soil

Recent reviews indicate that N deposition increases soil organic matter (SOM) storage in forests but the undelying processes are poorly understood. Our aim was to quantify the impacts of increased N inputs on soil C fluxes such as C mineralization and leaching of dissolved organic carbon (DOC) from different litter materials and native SOM. We added 5.5 g N m^?2 yr^?1 as NH₄NO₃ over 1 year to two beech forest stands on calcareous soils in the Swiss Jura. We replaced the native litter layer with ¹³C‐depleted twigs and leaves (δ¹³C: ?38.4 and ?40.8‰) in late fall and measured N effects on litter‐ and SOM‐derived C fluxes. Nitrogen addition did not significantly affect annual C losses through mineralization, but altered the temporal dynamics in litter mineralization: increased N inputs stimulated initial mineralization during winter (leaves: +25%; twigs: +22%), but suppressed rates in the subsequent summer. The switch from a positive to a negative response occurred earlier and more strongly for leaves than for twigs (?21% vs. 0%). Nitrogen addition did not influence microbial respiration from the nonlabeled calcareous mineral soil below the litter which contrasts with recent meta‐analysis primarily based on acidic soils. Leaching of DOC from the litter layer was not affected by NH₄NO₃ additions, but DOC fluxes from the mineral soils at 5 and 10 cm depth were significantly reduced by 17%. The ¹³C tracking indicated that litter‐derived C contributed less than 15% of the DOC flux from the mineral soil, with N additions not affecting this fraction. Hence, the suppressed DOC fluxes from the mineral soil at higher N inputs can be attributed to reduced mobilization of nonlitter derived ‘older’ DOC. We relate this decline to an altered solute chemistry by NH₄NO₃ additions, an increased ionic strength and acidification resulting from nitrification, rather than to a change in microbial decomposition.     

Nonparametric confidence interval estimators for heritability and expected selection response

Statistical methods have not been described for comparing estimates of family-mean heritability (H) or expected selection response (R), nor have consistently valid methods been described for estimating R intervals. Nonparametric methods, e.g., delete-one jackknifing, may be used to estimate variances, intervals, and hypothesis test statistics in estimation problems where parametric methods are unsuitable, nonrobust, or undefinable. Our objective was to evaluate normal-approximation jackknife interval estimators for H and R using Monte Carlo simulation. Simulations were done using normally distributed within-family effects and normally, uniformly, and exponentially distributed between-family effects. Realized coverage probabilities for jackknife interval (2) and parametric interval (5) for H were not significantly different from stated probabilities when between-family effects were normally distributed. Coverages for jackknife intervals (3) and (4) for R were not significantly different from stated coverages when between-family effects were normally distributed. Coverages for interval (3) for R were occasionally significantly less than stated when between-family effects were uniformly or exponentially distributed. Coverages for interval (2) for H were occasionally significantly less than stated when between-family effects were exponentially distributed. Thus, intervals (3) and (4) for R and (2) for H were robust. Means of analysis of variance estimates of R were often significantly less than parametric values when the number of families evaluated was 60 or less. Means of analysis of variance estimates of H were consistently significantly less than parametric values. Means of jackknife estimates of H calculated from log transformed point estimates and R calculated from untransformed or log transformed point estimates were not significantly different from parametric values. Thus, jackknife estimators of H and R were unbiased. Delete-one jackknifing is a robust, versatile, and effective statistical method when applied to estimation problems involving variance functions. Jackknifing is especially valuable in hypothesis test estimation problems where the objective is comparing estimates from different populations.     

More Accurate Dose-Response Estimation Using Monte-Carlo Uncertainty Analysis: The Data Cube Approach

The traditional q₁ ^* methodology for constructing upper confidence limits (UCLs) for the low-dose slopes of quantal dose-response functions has two limitations: (i) it is based on an asymptotic statistical result that has been shown via Monte Carlo simulation not to hold in practice for small, real bioassay experiments (Portier and Hoel, 1983); and (ii) it assumes that the multistage model (which represents cumulative hazard as a polynomial function of dose) is correct. This paper presents an uncertainty analysis approach for fitting dose-response functions to data that does not require specific parametric assumptions or depend on asymptotic results. It has the advantage that the resulting estimates of the dose-response function (and uncertainties about it) no longer depend on the validity of an assumed parametric family nor on the accuracy of the asymptotic approximation. The method derives posterior densities for the true response rates in the dose groups, rather than deriving posterior densities for model parameters, as in other Bayesian approaches (Sielken, 1991), or resampling the observed data points, as in the bootstrap and other resampling methods. It does so by conditioning constrained maximum-entropy priors on the observed data. Monte Carlo sampling of the posterior (constrained, conditioned) probability distributions generate values of response probabilities that might be observed if the experiment were repeated with very large sample sizes. A dose-response curve is fit to each such simulated dataset. If no parametric model has been specified, then a generalized representation (e.g., a power-series or orthonormal polynomial expansion) of the unknown dose-response function is fit to each simulated dataset using “model-free” methods. The simulation-based frequency distribution of all the dose-response curves fit to the simulated datasets yields a posterior distribution function for the low-dose slope of the dose-response curve. An upper confidence limit on the low-dose slope is obtained directly from this posterior distribution. This “Data Cube” procedure is illustrated with a real dataset for benzene, and is seen to produce more policy-relevant insights than does the traditional q₁ ^* methodology. For example, it shows how far apart are the 90%, 95%, and 99% limits and reveals how uncertainty about total and incremental risk vary with dose level (typically being dominated at low doses by uncertainty about the response of the control group, and being dominated at high doses by sampling variability). Strengths and limitations of the Data Cube approach are summarized, and potential decision-analytic applications to making better informed risk management decisions are briefly discussed.     

Simultaneous parsimony jackknife analysis of 2538rbcL DNA sequences reveals support for major clades of green plants, land plants, seed plants and flowering plants

The ever-larger data matrices resulting from continuing improvements in DNA sequencing techniques require faster and more efficient methods of phylogenetic analysis. Here we explore a promising new method, parsimony jackknifing, by analyzing a matrix comprising 2538 sequences of the chloroplast generbcL. The sequences included cover a broad taxonomic range, from cyanobacteria to flowering plants. Several parsimony jackknife analyses were performed, both with and without branch-swapping and multiple random addition sequences: 1) including all positions; 2) including only first and second codon positions; 3) including only third positions; and 4) using only transversions. The best resolution was obtained using all positions. Removal of third positions or transitions led to massive loss of resolution, although using only transversions somewhat improved basal resolution. While branch-swapping improved both resolution and the support found for several groups, most of the groups could be recovered by faster simple analyses. Designed to eliminate groups poorly supported by the data, parsimony jackknifing recognizes 1400 groups on the basis of allrbcL positions. These include major taxa such as green plants, land plants, flowering plants, monocots and eudicots. We include appendices of supported angiosperm families, as well as larger groups.