Quantitation of molecular densities by cryo-electron microscopy. Determination of the radial density distribution of tobacco mosaic virus.

We have determined the absolute mass and radial scattering density distribution of tobacco mosaic virus in the frozen-hydrated state by energy-filtered low-dose bright-field transmission electron microscopy. The absolute magnitude of electron scattering from tobacco mosaic virus in 150 nm of ice was within 3.0% of that predicted, with inelastic scattering accounting for approximately 80% of the scattering contrast. In order to test the accuracy of the radial reconstruction, a computer model of tobacco mosaic virus was built from the atomic co-ordinates assuming uniform solvent density. The validity of the model was confirmed by comparison of X-ray scattering and predictions of the model (R factor = 0.05). First-order corrections for the microscope contrast transfer function were necessary and sufficient for conversion of the cryo-electron microscopy images into accurate representations of the mass density. At 1.9 nm resolution the compensated reconstruction and model had density peaks of similar magnitude at 2.4, 4.2, 6.0 and 7.8 nm radius and a central hole of 2 nm radius. Equatorial Fourier transforms of the corrected electron images were in excellent agreement with predictions of the model (R factor = 0.12). Thus, the uniform solvent approximation was adequate at 1.9 nm resolution to describe quantitatively X-ray scattering in liquid water and electron imaging in vitreous ice. This is the first demonstration that cryo-electron microscopy images can be used to quantitate the absolute mass, mass per unit length and internal density distributions of proteins and nucleic acids.     

Effect of Moniliformis moniliformis density on distribution within the definitive host population (Rattus norvegicus)

The population dynamics of Moniliformis moniliformis was studied in ‘free-ranging’ laboratory rats, Rattus norvegicus, presented with different relative density levels of M. moniliformis in cockroaches, Periplaneta americana. Changes in selected population parameters of the negative binomial distribution were evaluated as indicators of changes in aggregation. A significant increase in the degree of aggregation of parasites occurred as a result of the increase in relative density of infective stages available to the rats. This increase in aggregation was due to the increase in over-dispersion that occurred in female rats only. The degree of aggregation in females was found to be significantly higher than that in males at both treatment levels. The best indicators of the degree of aggregation were found to be the ratio of the variance to the relative density and the ratio of the log-variance to log-relative density. Changes in k were not correlated with changes in over-dispersion or the relative density.     

The accuracy of the thermal dissipation technique for estimating sap flow is affected by the radial distribution of conduit diameter and density

There are conflicting reports on the accuracy of the thermal dissipation probe (TDP, the Granier method) measurement using the original formula, which is widely used to estimate the transpiration of individual trees and forest stands. In this article, six woody species of three wood types were used to study a possible association between TDP measurement accuracy and wood anatomical characteristics, including the vessel diameter and density, as well as sapwood depth. We found that TDP technique with Granier’s original equation underestimated the sap flux density in six species to various degrees, dependent on conduit size and sap flux. Our calibration using two conifers with small diameters and a high density of tracheids was relatively consistent with Granier’s calibration; however, because there were larger diameters and lower densities of vessels in the two diffuse-porous species, the original calibration significantly underestimated sap flow. Two ring-porous species had the largest diameters and lowest densities of vessels. In particular, Robinia pseudoacacia possessed the shallowest sap wood depth, less than a probe length. Our calibration for the ring-porous species, especially R. pseudoacacia, deviated far from the original calibration, which mostly underestimated the sap flow. The degree of underestimation was well associated with sap wood depth and the radial diameter and density distribution of conduits. Our results demonstrated that a new calibration must be operated for each species together with the sapwood depth determination and more probes may be applied for one stem in the field to obtain the more accurate sap flux. In addition, we investigated the effects of different environmental temperature and perfusing fluid composition on the TDP-based sap flux measurement. We found that an environmental temperature reduction from 25 to 0 °C did not alter the values of the maximum temperature difference (ΔT_m) between a heated probe and a reference probe when there was no sap flow, verifying that ΔT_m measured at night can be used as a reference in daytime.     

Effect of local spatial plant distribution and conspecific density on bumble bee foraging behaviour

1. Size variations in pollinator populations may modify competitive interactions among foragers. Competition among pollinators has been shown to lead to one of two contrasting behaviours: either specialisation to the most profitable plant species or generalisation to several species. When foraging, pollinators are also confronted with heterogeneity in the spatial distribution of plant resources. Because variations in both the forager density and plant spatial distribution can affect pollinator behaviour, focus was on the interactive effect of these two factors. 2. Bumble bee (Bombus terrestris L.) individuals were trained on a focal species (Lotus corniculatus L.) and experimentally tested whether variations in the forager density (two or six bumble bees foraging together), plant community spatial distribution (two plant species: L. corniculatus and Medicago sativa, which were either patchily or randomly distributed), and their interaction modified bumble bee foraging behaviour. 3. It was shown that when confronted with a high forager density, bumble bees focused their visits towards the most familiar species, especially when foraging under a random plant distribution. These modifications affected the fruiting of the focal plant species, with a significantly lower reproductive success under low density/patchy conditions. 4. This study demonstrates that the foraging decisions of bumble bees are influenced by variations in both the conspecific density and plant spatial distribution. Given the increasing impact of human activities on plant‐pollinator communities, this raises the question of the potential implications of these results for plant communities in natural conditions when confronted with variations in the pollinator density and spatial distribution of plants.     

Effect of the distribution and density of benthic target organisms on manta tow estimates of their abundance

The perception biases associated with manta tow estimates of the abundance of benthic organisms were investigated using artificial targets, the density, distribution and availability of which could be controlled. The proportion of targets which are counted by a mantatowed observer (sightability) and the precision of the resultant estimates of their abundance decreased as the targets were distributed more widely over a reef slope. The sightability of targets was enhanced when they were arranged at a high density or in relatively large groups of 9–11, or when they were located directly under the manta towed observer rather than at the edges of his visual field. Limiting the search width of a manta towed observer to about 9 m should improve manta tow estimates of target organisms. However, in practice this would be difficult for reef organisms such as Acanthaster planci because of the extreme three dimensionality of the reef surface relative to the depth of the water.     

Effect of list errors on the estimation of population size

In many situations, it is possible to estimate the size of a closed population if some members of the population are recorded on one or more administrative lists. An important example is estimating the prevalence of a disease, where some members of the disease population may be recorded on lists such as disease registries, hospital admission records, and general practitioner records. An incomplete contingency table is formed by matching the lists and the missing cell count estimated by prediction based on a fitted model, which assumes that the matching is done without error. In practice, matching errors do occur, and in this article, we examine the effect of these errors on the estimation process and show how the standard models may be modified to allow for matching errors.     

Effects of pressure on the composition density distribution in the ultracentrifuge

The effects of pressure on the composition density distribution in a binary density gradient at sedimentation equilibrium in the analytical ultracentrifuge are rigorously examined. A computer algorithm is described for the necessary iterative computations. The pressure effect is found to be significant in runs where a long column length, high angular velocity, and a salt with a high pressure correction coefficient are simultaneously employed. Such conditions are sometimes encountered in current studies in which high precision is required to measure the compressibility of proteins.     

On the distribution of developmental errors: comparing the normal, gamma, and log-normal distribution

The amount of between‐individual variation in the unobservable developmental instability (DI) has been the subject of intense recent debates. The unexpectedly high estimates of between‐individual variation in DI based on distributional characteristics of observable asymmetry values (of on average bilaterally symmetric traits) rely on statistical models that assume an underlying normal distribution of developmental errors. This prompted doubts on the assumption of the Gaussian nature of developmental errors. However, when applying other candidate distributions [log‐normal and gamma (γ)], recent analyses of empirical datasets have indicated that estimates remain generally high. Yet, all estimates were based on bilaterally symmetric traits, which did not allow for a formal comparison of the alternative distributions. In the present study, we extend a recent statistical model to allow statistical comparison of the different distributions based on traits that developed repeatedly under the same conditions, such as flower traits and regrown feathers. We analyse simulated and empirical data and show that: (1) it is statistically difficult to differentiate among the three alternatives when variances are small relative to the mean, as is often the case with DI; (2) the normal distribution fits the log‐normal or γ relatively well under those circumstances; (3) the deviance information criterion (DIC) is able to pick up differences in model fit among the three alternative distributions, yet more strongly so when levels of DI were high; (4) empirical datasets show a better fit of the normal over the log‐normal and γ‐distributions as judged by the DIC; and (5) estimates of between‐individual variation in DI in the three empirical datasets were relatively high (> 50%) under each distributional assumption. In conclusion, and based on our three datasets, the normal approximation appears to be a reasonable choice for statistical models of DI and the remarkably high estimates of variation in DI cannot be attributed to non‐normal developmental noise. Nevertheless, our method should be applied to a broad range of traits and organisms to evaluate the generality of this result. We argue that there is an urgent need for studies that reveal the underlying mechanisms of developmental noise and stability, as well as the role of developmental selection, in order to be able to determine the biological importance of the highly skewed distributions of developmental instability often observed. © 2007 The Linnean Society of London, Biological Journal of the Linnean Society, 2007, 92 , 197–210.     

Non-random chromosome distribution in radial metaphases from the Chinese hamster

Chromosome distribution was analyzed in uncultured radial metaphase cells (corneal epithelium, testicular mitotic cells, cells in diakinesis, and cells in metaphase II) from the Chinese hamster. The hypothesis of random distribution was rejected at the 0.001 level (x ₃ ² = 31.6). — Homologous association was observed for two pairs of chromosomes (3 and 10) in corneal epithelial cells. It was observed for all chromosomes in the testicular mitotic cells. Acrocentric association was observed in all four cell types. The chromosomes associated in four groups of similarly sized and shaped chromosomes. While group membership did not appear to vary, position within the group was highly variable. — An elevenpoint model of chromosome relationships was constructed from the data.     

Effect of colcemid on the radial spreading of fibroblasts in culture

Effect of colcemide upon the spreading of mouse embryo fibroblast-like cells on the substrate was studied with the aid of time-lapse microcinematography and scanning electron microscopy. On the glass, colcemide did not prevent the transition of cells into a well-attached state, however, the time needed for this transition was seen considerably increased as compared with the control cultures. Intermediate stages of spreading on flat glass had the following abnormal features in colcemide-containing medium: a) shapes of cytoplasmic outgrowths formed by the cell were altered and their distribution along the cell border appeared less regular; b) partial detachments of the attached parts of cells occurred very frequently; c) the spreading of various parts of the cells was not correlated. Possible mechanisms of colcemide action on the cell spreading are discussed, and it is suggested that intracellular structures sensitive to colcemide are essential for coordination of reactions that occur in various parts of the cell in the course of spreading.     

Geographical patterns in prediction errors of species distribution models

Aim To describe and explain geographical patterns of false absence and false presence prediction errors that occur when describing current plant species ranges with species distribution models. Location Europe. Methods We calibrated species distribution models (generalized linear models) using a set of climatic variables and gridded distribution data for 1065 vascular plant species from the Atlas Florae Europaeae. We used randomly selected subsets for each species with a constant prevalence of 0.5, modelled the distribution 1000 times, calculated weighted averages of the model parameters and used these to predict the current distribution in Europe. Using a threshold of 0.5, we derived presence/absence maps. Comparing observed and modelled species distribution, we calculated the false absence rates, i.e. species wrongly modelled as absent, and the false presence rates, i.e. species wrongly modelled as present, on a 50 × 50 km grid. Subsequently, we related both error rates to species range properties, land use and topographic variability within grid cells by means of simultaneous autoregressive models to correct for spatial autocorrelation. Results Grid‐cell‐specific error rates were not evenly distributed across Europe. The mean false absence rate was 0.16 ± 0.12 (standard deviation) and the mean false presence rate was 0.22 ± 0.13. False absence rates were highest in central Spain, the Alps and parts of south‐eastern Europe, while false presence rates were highest in northern Spain, France, Italy and south‐eastern Europe. False absence rates were high when range edges of species accumulated within a grid cell and when the intensity of human land use was high. False presence rates were positively associated with relative occurrence area and accumulation of range edges. Main conclusions Predictions for various species are not only accompanied by species‐specific but also by grid‐cell‐specific errors. The latter are associated with characteristics of the grid cells but also with range characteristics of occurring species. Uncertainties of predictive species distribution models are not equally distributed in space, and we would recommend accompanying maps of predicted distributions with a graphical representation of predictive performance.     

Progression of errors in morphometry. Estimation of particle number density

We have developed procedures whereby the progression of errors in various methods of morphometric data extrapolation may be evaluated. The analysis is straightforward and simple. We suggest that before collecting data, one should estimate the accepted fluctuations of the various parameters. Then, by calculation of propagation of errors, the most suitable method may be chosen, so that the data extracted will have an acceptable coefficient of variation. Higher precision carries a cost of time and/or money, and may not be necessary.