Zooming in on size distribution patterns underlying species coexistence in Baltic Sea phytoplankton

Scale is a key to determining which processes drive community structure. We analyse size distributions of phytoplankton to determine time scales at which we can observe either fixed environmental characteristics underlying communities structure or competition‐driven size distributions. Using multiple statistical tests, we characterise size distributions of phytoplankton from 20‐year time series in two sites of the Baltic Sea. At large temporal scales (5–20 years), size distributions are unimodal, indicating that fundamental barriers to existence are here subtler than in other systems. Frequency distributions of the average size of the species weighted by biovolume are multimodal over large time scales, although this is the product of often unimodal short‐term (<1 year) patterns. Our study represents a much‐needed structured, high‐resolution analysis of phytoplankton size distributions, revealing that short‐term analyses are necessary to determine if, and how, competition shapes them. Our results provide a stepping‐stone on which to further investigate the intricacies of competition and coexistence.     

Unimodal Tree Size Distributions Possibly Result from Relatively Strong Conservatism in Intermediate Size Classes

Tree size distributions have long been of interest to ecologists and foresters because they reflect fundamental demographic processes. Previous studies have assumed that size distributions are often associated with population trends or with the degree of shade tolerance. We tested these associations for 31 tree species in a 20 ha plot in a Dinghushan south subtropical forest in China. These species varied widely in growth form and shade-tolerance. We used 2005 and 2010 census data from that plot. We found that 23 species had reversed J shaped size distributions, and eight species had unimodal size distributions in 2005. On average, modal species had lower recruitment rates than reversed J species, while showing no significant difference in mortality rates, per capita population growth rates or shade-tolerance. We compared the observed size distributions with the equilibrium distributions projected from observed size-dependent growth and mortality. We found that observed distributions generally had the same shape as predicted equilibrium distributions in both unimodal and reversed J species, but there were statistically significant, important quantitative differences between observed and projected equilibrium size distributions in most species, suggesting that these populations are not at equilibrium and that this forest is changing over time. Almost all modal species had U-shaped size-dependent mortality and/or growth functions, with turning points of both mortality and growth at intermediate size classes close to the peak in the size distribution. These results show that modal size distributions do not necessarily indicate either population decline or shade-intolerance. Instead, the modal species in our study were characterized by a life history strategy of relatively strong conservatism in an intermediate size class, leading to very low growth and mortality in that size class, and thus to a peak in the size distribution at intermediate sizes.     

From snapshot information to long-term population dynamics of Acacias by a simulation model

The African Acacia species A. raddiana is believed to be endangered in the Negev desert of Israel. The ecology of this species is not well understood. The main idea of our study is to learn more about the long-term population dynamics of these trees using snapshot information in the form of size frequency distributions. These distributions are highly condensed indices of population dynamics acting over many years. In this paper, we analyse field data on recruitment, growth, and mortality and use an existing simulation model of the population dynamics of A. raddiana (SAM) to produce contrasting scenarios of these live history processes that are based on the analysed field evidence. The main properties of simulated as well as observed tree size frequency distributions are characterised with Simpson's index of dominance and a new permutation index. Finally, by running the SAM model under the different scenarios, we study the effect of these different processes on simulated size frequency distributions (pattern) and we compare them to size distributions observed in the field, in order to identify the processes acting in the field. Our study confirms rare recruitment events as a major factor shaping tree size frequency distributions and shows that the paucity of recruitment has been a normal feature of A. raddiana in the Negev over many years. Irregular growth, e.g., due to episodic rainfall, showed a moderate influence on size distributions. Finally, the size frequency distributions observed in the Negev reveal the information that, in this harsh environment, mortality of adult A. raddiana is independent of tree size (age).     

Mass extinctions do not explain skew in interspecific body size distributions

In several higher animal taxa, such as mammals and birds, the distribution of species body sizes is heavily skewed towards small size. Previous studies have suggested that small‐bodied organisms are less prone to extinction than large‐bodied species. If small body size is favourable during mass extinction events, a post mass extinction excess of small‐bodied species may proliferate and maintain skewed body size distributions sometime after. Here, we modelled mass extinctions and found that even unrealistically strong body mass selection has little effect on the skew of interspecific body size distributions. Moreover, selection against large body size may, counter intuitively, skew size distributions towards large body size. In any case, subsequent evolutionary diversification rapidly erases these rather small effects mass extinctions may have on size distributions. Next, we used body masses of extant species and phylogenetic methods to investigate possible changes in body size distributions across the Cretaceous–Paleogene (K‐Pg) mass extinction. Body size distributions of extant clades that originated during the Cretaceous are on average more skewed than their subclades that originated during the Paleogene, but the difference is only minor in mammals, and in birds, it can be explained by a positive relationship between species richness and skewness that is also present in clades that originated after the transition. Hence, we cannot infer from extant species whether the K‐Pg mass extinctions were size‐selective, but they are not the reason why most extant bird and mammal species are small‐bodied.     

Using size distributions to detect nutrient and sediment effects within and between habitats

We studied the use of size distributions as a response variable in limnological experiments. Previous quantifications of size distributions were incomplete or difficult to use in experimental settings, and we developed a multivariate approach that more fully describes the shape and biomass of planktonic and benthic size distributions. We re-evaluate the hypothesis that fish affect the shape and nutrients affect the biomass of size distributions, and show that the multivariate approach is more responsive to detecting treatment effects. In a mesocosm experiment, we use this new quantification and analysis of size distributions to detect the main and interactive effects of nutrient addition and sediment type on both benthic and pelagic size distributions. Size distributions in both habitats responded to the nutrient and sediment treatments, indicating linkage since a treatment applied in one habitat affected the size distribution in the opposite habitat. Since size distributions reduce each habitat into a common currency, we were able to examine the nature of the linkage. The relative response of each habitat to the nutrient treatment was different with regard to the shape of the distributions, while the relative response to the sediment treatment was different with regard to the biomass in the distributions.     

The effect of superspreading on epidemic outbreak size distributions

Recently, evidence has been presented to suggest that there are significant heterogeneities in the transmission of communicable diseases. Here, a stochastic simulation model of an epidemic process that allows for these heterogeneities is used to demonstrate the potentially considerable effect that heterogeneity of transmission will have on epidemic outbreak size distributions. Our simulation results agree well with approximations gained from the theory of branching processes. Outbreak size distributions have previously been used to infer basic epidemiological parameters. We show that if superspreading does occur then such distributions must be interpreted with care. The simulation results are discussed in relation to measles epidemics in isolated populations and in predominantly urban scenarios. The effect of three different disease control policies on outbreak size distributions are shown for varying levels of heterogeneity and disease control effort.     

Environmental correlates of body size distributions of European springtails (Hexapoda: Collembola)

Aim Species–body size distributions (SBDs) are plots of species richness across body size classes. They have been linked to energetic constraints, speciation–extinction dynamics and to evolutionary trends. However, little is known about the spatial variation of size distributions. Here we study SBDs of European springtails (Collembola) at a continental scale and test whether minimum, average and maximum body size and the shapes of size distributions change across latitudinal and longitudinal gradients and whether SBDs of islands and mainlands differ. We also test whether the island rule and the positive body size–range size relationship of vertebrates also holds for Collembola. Location Europe. Methods We use a unique data set on the spatial distributions of 2102 species of European springtails across 52 countries and larger islands together with associated data on body size, area, climate variables, longitude and latitude. Differences in the central moments of SBDs are inferred from simultaneous spatial autoregression models. Results The SBD of the European Collembola and its largest suborder Entomobryomorpha is unimodal and symmetrical. Average, minimum and maximum body weight and the skewness of the mainland/island SBDs peaked at intermediate latitudes. We could not find simple latitudinal gradients in minimum and maximum body weight. Average and maximum body size increased with country/island area in accordance with the island rule in vertebrates, while minimum body size did not significantly differ between islands and mainlands. Finally, we found a weak but statistically significant positive correlation of range size and body size. Main conclusions We provide evidence for differences in body size distributions between islands and mainlands that are in part in line with the island rule in invertebrates. We also find evidence for an interspecific body size–range size relationship similar to that of vertebrates although the vertebrate pattern is much stronger than the springtail pattern. Our results on latitudinal gradients of maximum and average body size imply the need to account for species richness and area effects in the study of latitudinal gradients in body size. We recommend implementing sample size and area effects in the study of body size distributions on islands and mainlands.     

Liposome filtration. Dependence on transition temperature

Liposomes formed by vortexing and passed through polycarbonate surface retention membranes showed appreciable differences in filtration behavior depending on the temperature of filtration relative to the liposome gel-liquid crystal transition temperature. Below transition, liposomes were filterable and size distributions could be determined; the cumulative volume distributions were log-normal. Above transition, liposomes were not filterable: smaller liposomes were formed until a limiting size was reached. These results suggest that liquid crystal liposome size distributions cannot be determined by filtration. This filtration behavior is a physical property of liposomes, related to the gel-liquid crystal transition, not previously reported. This property could be exploited as a new method for controlling liposome size distributions, but the implications for lipid membranes, including biological membranes, are general.     

Model calculations of casein micelle size distributions.

A previously proposed model for the formation and structure of casein micelles from subunits of variable composition is used to calculate theoretical micelle size distributions. Using the fractional content of k-casein as the only variable but with a value near that observed in a sample of milk serum, the model successfully reproduces experimentally determined distributions. Predicted size distributions are quite sensitive to the value of the variable and shift toward smaller average size as the assumed fractional content k-casein gets larger. Also, there is a discontinuity in the distributions which predicts that there will be essentially no micelles with radii smaller than 25-30 nm. These predictions are all in accord with experimental observations. The good agreement between theory and experimenet supports the micelle structure suggested by the model.     

Tree size distributions in an old-growth temperate forest

Despite the wide variation in the structural characteristics in natural forests, tree size distribution show fundamental similarities that suggest general underlying principles. The metabolic ecology theory predicts the number of individual scales as the −2 power of tree diameter. The demographic equilibrium theory predicts tree size distribution starting from the relationship of size distributions with growth and mortality at demographic equilibrium. Several analytic predictions for tree size distributions are derived from the demographic equilibrium theory, based on different growth and mortality functions. In addition, some purely phenomenological functions, such as polynomial function, have been used to describe the tree size distributions. In this paper, we use the metabolic ecology theory, the demographic equilibrium theory and the polynomial function to predict the tree size distribution for both the whole community and each species in an old-growth temperate forest in northeastern China. The results show that metabolic ecology theory predictions for the scaling of tree abundance with diameter were unequivocally rejected in the studied forest. Although these predictions of demographic theory are the best models for most of the species in the temperate forest, the best models for some species ( Tilia amurensis , Quercus mongolica and Fraxinus mandshurica ) are compound curves (i.e. rotated sigmoid curves), best predicted by the polynomial function. Hence, the size distributions of natural forests were unlikely to be invariant and the predictive ability of general models was limited. As a result, developing a more sophisticated theory to predict tree size distributions remains a complex, yet tantalizing, challenge.     

New Ranked Set Sampling for One‐Parameter Family of Distributions

Bhoj (1997c) proposed a new ranked set sampling (NRSS) procedure for a specific two‐parameter family of distributions when the sample size is even. This NRSS procedure can be applied to one‐parameter family of distributions when the sample size is even. However, this procedure cannot be used if the sample size is odd. Therefore, in this paper, we propose a modified version of the NRSS procedure which can be used for one‐parameter distributions when the sample size is odd. Simple estimator for the parameter based on proposed NRSS is derived. The relative precisions of this estimator are higher than those of other estimators which are based on other ranked set sampling procedures and the best linear unbiased estimator using all order statistics.     

Characterization of Nanocrystal Size Distribution using Raman Spectroscopy with a Multi-particle Phonon Confinement Model

Analysis of the size distribution of nanocrystals is a critical requirement for the processing and optimization of their size-dependent properties. The common techniques used for the size analysis are transmission electron microscopy (TEM), X-ray diffraction (XRD) and photoluminescence spectroscopy (PL). These techniques, however, are not suitable for analyzing the nanocrystal size distribution in a fast, non-destructive and a reliable manner at the same time. Our aim in this work is to demonstrate that size distribution of semiconductor nanocrystals that are subject to size-dependent phonon confinement effects, can be quantitatively estimated in a non-destructive, fast and reliable manner using Raman spectroscopy. Moreover, mixed size distributions can be separately probed, and their respective volumetric ratios can be estimated using this technique. In order to analyze the size distribution, we have formulized an analytical expression of one-particle PCM and projected it onto a generic distribution function that will represent the size distribution of analyzed nanocrystal. As a model experiment, we have analyzed the size distribution of free-standing silicon nanocrystals (Si-NCs) with multi-modal size distributions. The estimated size distributions are in excellent agreement with TEM and PL results, revealing the reliability of our model.     

Evolution, Ecology, and Multimodal Distributions of Body Size

The sizes of organisms are determined by their interactions with their environment and related ecological and evolutionary processes. Recent studies of body size distributions across communities show evidence for multimodality. The multiple modes were originally explained as a consequence of textural discontinuities in habitat structure. Because communities consist of species that are drawn from lineages, body size patterns within lineages will affect those that are expressed in communities. We used a cellular automation model to argue that multimodality in body sizes within lineages can arise from a few fundamental evolutionary mechanisms alone. We tested the hypothesis using body size data for 138 fish genera and found strong support for the idea that evolution structures body size distributions. The results suggest, first, that we should expect the distribution of body sizes within lineages to be multimodal and second, that a coherent theory of community body size distributions will need to combine both evolutionary and ecological perspectives. Received 28 January 2002; accepted 21 March 2002     

Species-range size distributions in Britain

The detailed forms of species-range size distributions in Britain are determined and contrasted for ten taxonomic assemblages (liverworts, vascular plants, molluscs [aquatic and terrestrial], dragonflies, macro-moths. butterflies, birds [breeding and wintering], mammals). All are strongly right-skewed when range sizes are untransformed. A logarithmic transformation fails to normalise the distribution for all but one group, and the distributions for several groups are not readily normalised at all. Taxa with larger median range sizes have species-range size distributions that are less strongly right-skewed. The median observed range sizes of species in each of the taxonomic groups fall, in terms of decreasing range size, in the sequence wintering birds < breeding birds < mammals < butterflies < terrestrial molluscs < dragonflies < aquatic molluscs < vascular plants < moths < liverworts. Despite the difficulties in deriving a simple and sensible mechanistic model for range size distributions, this is likely to be the most important next step towards understanding their forms.     

Habitat structure and body size distributions: cross‐ecosystem comparison for taxa with determinate and indeterminate growth

Habitat structure across multiple spatial and temporal scales has been proposed as a key driver of body size distributions for associated communities. Thus, understanding the relationship between habitat and body size is fundamental to developing predictions regarding the influence of habitat change on animal communities. Much of the work assessing the relationship between habitat structure and body size distributions has focused on terrestrial taxa with determinate growth, and has primarily analysed discontinuities (gaps) in the distribution of species mean sizes (species size relationships or SSRs). The suitability of this approach for taxa with indeterminate growth has yet to be determined. We provide a cross‐ecosystem comparison of bird (determinate growth) and fish (indeterminate growth) body mass distributions using four independent data sets. We evaluate three size distribution indices: SSRs, species size–density relationships (SSDRs) and individual size–density relationships (ISDRs), and two types of analysis: looking for either discontinuities or abundance patterns and multi‐modality in the distributions. To assess the respective suitability of these three indices and two analytical approaches for understanding habitat–size relationships in different ecosystems, we compare their ability to differentiate bird or fish communities found within contrasting habitat conditions. All three indices of body size distribution are useful for examining the relationship between cross‐scale patterns of habitat structure and size for species with determinate growth, such as birds. In contrast, for species with indeterminate growth such as fish, the relationship between habitat structure and body size may be masked when using mean summary metrics, and thus individual‐level data (ISDRs) are more useful. Furthermore, ISDRs, which have traditionally been used to study aquatic systems, present a potentially useful common currency for comparing body size distributions across terrestrial and aquatic ecosystems.     

Disentangling the influences of mean body size and size structure on ecosystem functioning: an example of nutrient recycling by a non‐native crayfish

Body size is a fundamental functional trait that can be used to forecast individuals' responses to environmental change and their contribution to ecosystem functioning. However, information on the mean and variation of size distributions often confound one another when relating body size to aggregate functioning. Given that size‐based metrics are used as indicators of ecosystem status, it is important to identify the specific aspects of size distributions that mediate ecosystem functioning. Our goal was to simultaneously account for the mean, variance, and shape of size distributions when relating body size to aggregate ecosystem functioning. We take advantage of habitat‐specific differences in size distributions to estimate nutrient recycling by a non‐native crayfish using mean‐field and variance‐incorporating approaches. Crayfishes often substantially influence ecosystem functioning through their omnivorous role in aquatic food webs. As predicted from Jensen's inequality, considering only the mean body size of crayfish overestimated aggregate effects on ecosystem functioning. This bias declined with mean body size such that mean‐field and variance‐incorporating estimates of ecosystem functioning were similar for samples at mean body sizes >7.5 g. At low mean body size, mean‐field bias in ecosystem functioning mismatch predictions from Jensen's inequality, likely because of the increasing skewness of the size distribution. Our findings support the prediction that variance around the mean can alter the relationship between body size and ecosystem functioning, especially at low mean body size. However, methods to account for mean‐field bias performed poorly in samples with highly skewed distributions, indicating that changes in the shape of the distribution, in addition to the variance, may confound mean‐based estimates of ecosystem functioning. Given that many biological functions scale allometrically, explicitly defining and experimentally or statistically isolating the effects of the mean, variance, and shape of size distributions is necessary to begin generalizing relationships between animal body size and ecosystem functioning.     

Cell growth and division: a deterministic/probabilistic model of the cell cycle

A model of the cell cycle, incorporating a deterministic cell-size monitor and a probabilistic component, is investigated. Steady-state distributions for cell size and generation time are calculated and shown to be globally asymptotically stable. These distributions are used to calculate various statistical quantities, which are then compared to known experimental data. Finally, the results are compared to distributions calculated from a Monte-Carlo simulation of the model.     

Is the Rapoport effect widespread? Null models revisited

Aim  To test the Rapoport effect using null models and data sets taken from the literature. We propose an improvement on an existing method, testing the Rapoport effect in elevational and latitudinal distributions when distributions are restricted by sampling.
Location  Global.
Methods  First, we hypothesized that real range size distributions are similar to those expected by null assumptions (expected by only imposing boundaries to species distributions). When these distributions were different from those expected under the null assumptions, we tested the hypothesis that these distributions correspond to those expected when a Rapoport effect occurs. We used two simulation methods, random and pseudo-random, which differed only in that the latter one assumes fixed species mid-points, coinciding with real mid-points. Observed correlations between range size and mid-point were compared with the frequency distribution of 1000 simulations, using both simulation methods. We compared the correlation curves generated by 1000 simulations with those of the observed distributions, testing whether correlations indicated a Rapoport effect.
Results  Several significant patterns of correlations between range size and mid-point were observed in the data sets when compared with random and pseudo-random simulations. However, few of these correlations were consistent with a Rapoport effect.
Main conclusions  Although some recent studies are consistent with a Rapoport effect, our results suggest that the Rapoport effect is not a widespread pattern in global ecology.     

Measurement of bubble and pellet size distributions: past and current image analysis technology

Measurements of bubble and pellet size distributions are useful for biochemical process optimizations. The accuracy, representation, and simplicity of these measurements improve when the measurement is performed on-line and in situ rather than off-line using a sample. Historical and currently available measurement systems for photographic methods are summarized for bubble and pellet (morphology) measurement applications. Applications to cells, mycelia, and pellets measurements have driven key technological developments that have been applied for bubble measurements. Measurement trade-offs exist to maximize accuracy, extend range, and attain reasonable cycle times. Mathematical characterization of distributions using standard statistical techniques is straightforward, facilitating data presentation and analysis. For the specific application of bubble size distributions, selected bioreactor operating parameters and physicochemical conditions alter distributions. Empirical relationships have been established in some cases where sufficient data have been collected. In addition, parameters and conditions with substantial effects on bubble size distributions were identified and their relative effects quantified. This information was used to guide required accuracy and precision targets for bubble size distribution measurements from newly developed novel on-line and in situ bubble measurement devices.