Individual Size Distribution Research Articles

On The Expected Discounted Penalty function for Lévy Risk Processes

Dufresne et al. (1991) introduced a general risk model defined as the limit of compound Poisson processes. Such a model is either a compound Poisson process itself or a process with an infinite number of small jumps. Later, in a series of now classical papers, the joint distribution of the time of ruin, the surplus before ruin, and the deficit at ruin was studied (Gerber and Shiu 1997, 1998a, 1998b; Gerber and Landry 1998). These works use the classical and the perturbed risk models and hint that the results can be extended to gamma and inverse Gaussian risk processes. In this paper we work out this extension to a generalized risk model driven by a nondecreasing Lévy process. Unlike the classical case that models the individual claim size distribution and obtains from it the aggregate claims distribution, here the aggregate claims distribution is known in closed form. It is simply the one-dimensional distribution of a subordinator. Embedded in this wide family of risk models we find the gamma, inverse Gaussian, and generalized inverse Gaussian processes. Expressions for the Gerber-Shiu function are given in some of these special cases, and numerical illustrations are provided.

A photographic gap fraction method for estimating leaf area of isolated trees: assessment with 3D digitized plants

A method for computing leaf area of isolated trees from perspective photographs was developed. The method is based on gap fraction inversion. Photographs are discretized into picture zones where gap fraction is computed from image processing. Canopy volume and leaf area density associated with each picture zone are computed from geometrical considerations and inversion of gap fraction equations. Total leaf area and the vertical profile of leaf area are computed from the product of associated volume and its density. The method has been implemented in software called Tree Analyser, written in C++. The method has been tested by comparison with direct estimation of leaf area of three-dimensional (3D) digitized trees of walnut, peach, mango, olive and rubber. Estimated leaf area was sensitive to picture discretization, individual leaf size and leaf inclination distribution. Optimal size of picture discretization was 17 times projected leaf size. Total leaf area was estimated by using a set of eight photographs taken around the tree in the main horizontal directions: deviation ranged from -11% in peach tree to +5% in rubber tree. The method allows fast and nondestructive monitoring of leaf area of individual tree canopies. The next version of the method will include the estimation of 3D leaf area distribution within the canopy.

Spatio-Temporal Distribution of Freshwater Snail Species in Relation to Migration and Environmental Factors in an Irrigated Area from Morocco

Nine sites were sampled 19 times over 2 years in an irrigation system in Morocco in order to study species abundance in a snail community in relation to environmental parameters (including human activities) and migration (geographic distance) among sites. Each site was made of a sink and the first meters of the downstream canal. The snail community included four species (Bulinus truncatus, Lymnaea truncatula, Mercuria similis and Physa acuta). Strong spatial variation in species occurrence and abundance was detected which might be partly due to variation in water availability. However abundance in sinks and canals in which water availability differs were correlated. There was, as predicted, limited evidence in favor of isolation by distance which might be due to fast water current. Dispersal might therefore be an important factor structuring this community. On the other hand, the temporal variation was much more limited. This is consistent with the analysis of individual size distributions in B. truncatus, since no clear-cut cohorts were detected. The environmental parameters recorded (e.g. temperature, occurrence of macrophytes or cleaning of sinks) were extremely variable in time and space, except temperature. Analyzing their association with species through multidimensional methods indicated that P. acuta is ubiquitous and B. truncatus positively associated with macrophytes. These two species were associated in sinks. Less clear trends were detected for the two other species. Annual cleaning of sinks affected all species, but population recovery was fast in B. truncatus and P. acuta.

Broadening of droplet size distributions from entrainment and mixing in a cumulus cloud

Quantitative predictions of the relationship between the droplet size-distribution width and entrainment in warm cumulus have been elusive, largely because of the difficulty in representing the extent of the scales involved. A new modelling framework is presented as a first step toward quantitative predictions of droplet size distributions resulting from entrainment, consisting of a three-dimensional cloud model coupled with a Lagrangian microphysical parcel model. The cloud model represents turbulent cloud dynamics but parametrizes microphysical processes such as condensation, and the parcel model complements this approach by performing explicit microphysical calculations within the kinematic and thermodynamic constraints established by the cloud model. The parcel model is run along trajectories all ending at the same point in the cloud, and the individual droplet size distributions are averaged together at this point to represent the turbulent mixing together of the droplets produced by these different parcel trajectories. The results replicate some important features of observed cloud droplet size distributions, including large widths, the continued presence of small droplets high in the clouds, and the bimodal structure. The origin of these features in these calculations is the variability introduced by entrainment, which leads to possibilities for droplets to encounter varying supersaturation histories during their transit through the cloud to the point of observation. Droplet sizes larger than those calculated for adiabatic ascent are also produced, with possible implications for coalescence initiation. Copyright © 2005 Royal Meteorological Society

Molecular modeling of binary mixtures of amphiphiles in a lattice solution

We examine the behavior of binary surfactant mixtures using Monte Carlo simulations with a three-dimensional lattice model of a binary surfactant mixture, in which the surfactants are represented by a series of connected beads. The range of amphiphile concentrations used is around the critical micelle concentration. The quasichemical approximation, a mean-field lattice theory, has also been used to determine the phase equilibrium for these types of solutions. The simulations allow direct determination of micellar properties such as the composition of the aggregates and dispersed phase as well as the individual size distribution of the amphiphiles in the aggregates. Properties of the aggregates such as their shapes, sizes, and volume fraction profiles have also been calculated. The simulation results are analyzed in light of the phase separation model, which considers the micelles as a separate bulk pseudo-phase. The Monte Carlo calculations show that even though the thermodynamic assumptions behind the regular solution theory are not correct, it can be very useful in approximating the prediction of the monomer-micelle compositions and the amphiphile activity coefficients in micelles for mixed amphiphile systems. The results of the simulations do not satisfy fully a thermodynamic consistency test based on the Gibbs–Duhem relationship. This raises questions about the application of the pseudo-phase model to mixed surfactant systems at the concentrations investigated in this work. One potential reason for the noncompliance of this test is that the aggregates might be too small to be considered a pseudo-phase.

The polarimetric properties of cometary dust and a possible effect of dust aging by the Sun

After the last apparition of comet Halley in 1985-86, a number of other comets were observed in polarimetry with IHW-continuum filters. From the in situ dust measurements of Halley, dust size distribution functions were obtained (Lamy et al. 1987, AA Mazets et al. 1986, Nature, 321, 276), which were later used by several authors to interpret polarisation data of Halley. In the present work, polarimetric data of various comets have been analyzed, using Mie theory and assuming that the composition of dust particles does not differ from comet to comet (Delsemme 1987, ESA SP-278, 19). The individual grain size distribution functions so obtained for various comets suggest different values for the abundance of coarser grains. Introducing a relative abundance of coarser index g, we study any possible dependence of g on the dynamical age of a comet, where the dynamical age can be defined in terms of some of the orbital parameters of the comet. For the four non-periodic comets available for our analysis, we find a clear empirical relation g = −2.5.q 2/3 emerging from our work. This relation strengthens the concept that comets whose grains are processed more by the solar radiation (these comets may be dynamically older) contain a relatively smaller number of finer grains. The case for other periodic comets is also discussed here. Since the work has been carried out using Mie scattering theory meant for perfect compact spheres, it is also suggested to repeat the calculations with more realistic porous grains in a follow-up paper.

GAP-DEPENDENT RECRUITMENT, REALIZED VITAL RATES, AND SIZE DISTRIBUTIONS OF TROPICAL TREES

In closed-canopy forests, plant morphology and physiology determine shade tolerance and potential growth and mortality rates; potential vital rates and ongoing gap dependence determine realized vital rates; and realized vital rates determine individual size distributions. This hypothesis was evaluated for the 73 most abundant canopy tree species from Barro Colorado Island, Panama. The percentage of recruits located in tree-fall gaps (P), sapling growth (G), and mortality (M) rates, and the coefficient of skewness of size distributions (g1) were determined from censuses of all individuals >10 mm dbh in a 50-ha plot. Seven qualitative, bivariate predictions relating g1, G, M, P, and wood density (W) were evaluated. Six of the seven predictions were substantiated in pairwise analyses. A path analysis integrated all seven predictions and explained 51% of the interspecific variation in g1. Size distributions with many large individuals and a long tail of relatively rare, small individuals (g1 < 0) characterized gap-dependent species with large fecundity, seed mortality, seedling mortality, G, M, and P. Size distributions with many small individuals and a long tail of relatively rare, large individuals (g1 > 0) characterized shade-tolerant species with the opposite traits. The percentage of tropical tree species that require tree-fall gaps to regenerate has been estimated to range from <20% to >70% for old-growth forests. Our analyses suggest that there are not large numbers of functionally equivalent species at either extreme of the regeneration continuum. Rather, there are very few extremely shade-tolerant and extremely light-demanding species. Most species have intermediate light requirements and lifestyles.

Using the Survivor Technique to Estimate Returns to Scale and Optimum Firm Size

Abstract The survivor technique for estimating returns to scale and optimum firm size has generated a slow but steady literature since its 1958 pilot presentation by George Stigler. This article (1) integrates advances in its application into a complete demonstration of how the technique works, (2) distinguishes a survivor analysis from the related but different analyses of individual firm growth and size distribution as addressed, for example, by Gibrat's Law of Proportionate Effect, (3) surveys a few exemplary survivor analyses, highlighting their alternative measures of scale and survival, and (4) unifies the scattered discussion of criticisms and qualifications that surround the technique. Accordingly, this essay seeks to reposition the survivor technique as a viable statistical option for research on those industries which meet its criteria.

INDIVIDUAL VARIATION AND ENVIRONMENTAL STOCHASTICITY: IMPLICATIONS FOR MATRIX MODEL PREDICTIONS

Populations are characterized by variability among individuals, a result of both intrinsic differences among individuals and environmental effects on individual performance. Despite the ubiquity of individual variation, its implications for population model choice are not fully understood. Population models that use state variables representing individual features such as age or size assume that these state variables can predict the population trajectory. However, state variables are often chosen based on convenience or necessity; only rarely are they tested for importance and accuracy when individuals vary. We examined whether matrix projection models, a common choice in population modeling, provide accurate predictions when individuals vary in a population. With both density-dependent and density-independent formulations, we tested whether matrix projection models that used size as a state variable captured the dynamics of populations projected with an individual-based simulation (or i-state configuration model). We varied the initial size distribution of individuals, the degree to which individual growth was size dependent, the tendency for positive correlations in growth through time, and the amount of stochasticity in growth, and we asked what conditions affect the accuracy of matrix models. Stochasticity alone did not compromise the predictions of matrix models; rather, only populations with individual variation generated by strong size-dependent growth and growth correlations were poorly described by matrix models. Otherwise, matrix models captured the trajectories of populations with a fair degree of accuracy. Overall, our results provide guidance as to when and how individual variation must be included in population projections, and when a simple matrix model framework is inadequate. Corresponding Editor: A. R. Solow

Selective feeding by larval dytiscids (Coleoptera:Dytiscidae) and effects of fish predation on upper littoral zone macroinvertebrate communities of arctic lakes

Upper littoral zones of 13 lakes with fish and 10 lakes without fish were sampled to compare macroinvertebrate communities. Lakes with fish had lower macroinvertebrate species richness, diversity, and smaller-sized individuals than lakes without fish. Larger invertebrates, including most large invertebrate predators, such as dytiscids, corixids, odonates, Gammarus, and Chaoborus, were generally not found in lakes with fish. To determine the feeding behavior of a conspicuous invertebrate predator found in fishless lakes, the predaceous diving beetle (Coleoptera: Dytiscidae), we used microcosm feeding experiments and a molecular technique for gut content analysis. Dytiscids were sit-and-wait predators in the laboratory, feeding on large, mobile species and avoiding smaller, benthic species. Gut content analyses of field-caught dytiscids, as assessed by native polyacrylamide gel electrophoresis, were not entirely consistent with laboratory selectivity studies, but the field results did confirm that dytiscids fed on large mobile species. However, we cannot rule out the possibility that small prey might also have been ingested. We conclude that fish impact macroinvertebrate diversity in the upper littoral zones of these arctic lakes by excluding large invertebrates and decreasing species richness, diversity, and size-distribution of individuals. Dytiscids in fishless lakes feed on large species as well, but clearly do not eliminate them from lakes as do fish.

Lipopolysaccharides from Mesorhizobium huakuii and Mesorhizobium ciceri: chemical and immunological comparative data.

Lipopolysaccharides of two Mesorhizobium species of different host specificity were compared: M. huakuii and M. ciceri. M. huakuii sp. was represented by five strains with special consideration of M. huakuii IFO 15243(T). SDS/PAGE profiles revealed that all M. huakuii LPS preparations contained low molecular mass fractions (LPS-II) of the same molecular size. All of lipopolysaccharides contained high molecular mass fractions (LPS-I). However, the high molecular mass fraction from each strain possessed an individual molecular size distribution pattern. The crossreactivity of blotted lipopolysaccharides with rabbit polyclonal antibodies against Mesorhizobium huakuii IFO 15243(T) whole bacteria indicated the presence of common epitope(s) within the investigated Mesorhizobium huakuii strains. Moreover, LPS from M. huakuii S52 also reacted with anti M. ciceri HAMBI 1750 serum showing that there are epitopes common for different mesorhizobial species. LPS isolated from Mesorhizobium huakuii strain IFO 15243(T) contained neutral sugars: L-6-deoxytalose, L-rhamnose, D-galactose and D-glucose, aminosugars:D-quinovosamine, D-glucosamine, D-2,3-diamino-2,3-dideoxyglucose and D-galacturonic and D-glucuronic acids. In the LPS preparation, fatty acids typical for Mesorhizobium strains were detected. 3-Hydroxydodecanoic, 3-hydroxy-iso-tridecanoic, 3-hydroxyeicosanoic, 3-hydroxyheneicosanoic and 3-hydroxydocosenoic acids were the major amide linked fatty acids, while iso -heptadecanoic, eicosanoic, docosenoic, as well as 27-hydroxyoctacosanoic and 27-oxooctacosanoic acids were the dominant ester linked fatty residues.

Classifying human endothelial cells based on individual granulometric size distributions

Abstract This paper presents an application to a medical problem of methods of shape analysis based on mathematical morphology. The medical problem consists on the detection of abnormalities in the corneal endothelium, a tissue composed by quasi-planar cells of ideally regular hexagonal shape. Images of this tissue are taken by a specular microscope and used to evaluate the corneal endothelium status. Up to now, cell density, hexagonality and an analysis of cell areas are the usual descriptors of a corneal endothelium. These parameters are not sensitive enough to detect subtle lesions. What this paper proposes is an analysis based on granulometries, which are size-shape descriptors widely used in Mathematical Morphology. Applications of granulometries lead to distribution functions whose moments are used as shape descriptors. Former approaches proposed a global evaluation of the whole corneal endothelium but irregularities affecting to a few cells could be ignored. Differently to that approach, this paper uses the granulometric size distribution of each cell. A group of normal cells is chosen as controls and a given cell is classified as normal or abnormal by comparing its granulometric size distribution with the corresponding distributions of the controls. The technique is illustrated with the analysis of some images of corneal endothelia.

LENGTH DYNAMICS IN JUVENILE COASTAL SKAGERRAK COD: EFFECTS OF BIOTIC AND ABIOTIC PROCESSES

Individual growth and size distributions within populations are generally influenced by both biotic and abiotic factors. Positively skewed size distributions may arise as a result of any size-selective process, such as food scarcity or competition. While such patterns have been observed for a variety of terrestrial plant and animal species, size distribution has been less studied for marine fish in the natural environment. This we do in the present paper. In order to investigate the effect of density and environment on juvenile coastal cod (Gadus morhua L.), we assess the length distributions of fish caught at fixed locations along the southern Norwegian Skagerrak coast over the period 1919–1996. We demonstrate that most distributions are skewed to the right, suggesting that competition may influence these systems; such effects seem to be strongest for sheltered stations inside the fjords. Density dependence is inferred as skewness increases with increased density, and the average length decreases with increased density. The skewness, average length, and abundance of juvenile cod caught in the autumn are shown to be influenced by the meteorological conditions in the spring (i.e., during the larval period). Directional wind stress along the shore and toward the shore and high temperatures create favorable conditions for the development of cod larvae. The effects of local abiotic factors may be measured through the North Atlantic Oscillation (NAO) Index, a large-scale climatic proxy.

Application of volume growth and survival graphs in the evaluation of four process-based forest growth models.

Volume growth and survival (VGS) graphs, which show volume growth rate and risk of mortality for individual trees (or tree size classes), have been proposed as a tool for assessing the validity of models that describe the development over time of tree size distributions within forest stands. We examined the utility of the VGS method in evaluating four process-based models. The performance of the models FORSKA, 4C, MORG, and PipeQual is analyzed against long-term data from a Scots pine stand in Evo, Finland, and the models FORSKA and 4C are also assessed with respect to data from a beech stand in Fabrikschleichach, Germany. Comparison of the measurement-based VGS graphs with those produced from the model-based data shows that although the models yield similar stand-level predictions, they can differ widely in their projections of individual tree growth and size distributions. Examination of the discrepancies between models and data in the context of the VGS graphs reveals several areas in which the models could be improved. We conclude that the method is useful in model evaluation, especially if used in combination with indicators of stand structure, such as the height/diameter ratio.

Factors affecting the occurrence of early maturing males in the protandrous pandalid shrimp Pandalus latirostris

Some Age-0 males of the protandrous pandalid shrimp Pandalus latirostris Rathbun mature in their first year, and the proportion of these early maturing males (EMMs) in a population varies both locally and annually. Two laboratory experiments and 2 field observations were con- ducted to clarify the factors affecting the occurrence of EMMs. The first experiment showed that EMMs needed to grow fast until the breeding season and began producing sperm at about 14 mm carapace length. Individuals with an AMP (length of the endopod/length of the appendix masculina) value above 40 were defined as EMMs. In the second experiment, the effects of food amount, hatch- ing date and maternal size on growth at Age-0 were examined. Food amount strongly affected the early growth. A difference in hatching date of >2 wk caused a large difference in body size of juve- niles; this difference was maintained until the breeding season 3 mo later. Large females spawned larger larvae than small females, but the size difference between larvae from large females and those from small females decreased with time. Field observations showed that at one site in Saroma Lagoon, Hokkaido, Japan, hatching occurred over a 1 mo period. In 1996/1997, we found no obvious differences of size distribution of Age-0 individuals and the occurrence of EMM as a function of loca- tion in the lagoon or year. These results may have been caused by slow growth, because water tem- peratures in the lagoon were much colder in 1996/1997 than during 1987 to 1995. We conclude that the occurrence of EMMs is closely related to various environmental factors in shallow waters. There- fore, the proportion of EMMs may fluctuate both locally and annually. This study shows that a small difference in juvenile growth over a short period can alter the subsequent life history of P. latirostris.

The application of mass and energy conservation laws in physiologically structured population models of heterotrophic organisms

Rules for energy uptake, and subsequent utilization, form the basis of population dynamics and, therefore, explain the dynamics of the ecosystem structure in terms of changes in standing crops and size distributions of individuals. Mass fluxes are concomitant with energy flows and delineate functional aspects of ecosystems by defining the roles of individuals and populations. The assumption of homeostasis of body components, and an assumption about the general structure of energy budgets, imply that mass fluxes can be written as weighted sums of three organizing energy fluxes with the weight coefficients determined by the conservation law of mass. These energy fluxes are assimilation, maintenance and growth, and provide a theoretical underpinning of the widely applied empirical method of indirect calorimetry, which relates dissipating heat linearly to three mass fluxes: carbon dioxide production, oxygen consumption and N-waste production. A generic approach to the stoichiometry of population energetics from the perspective of the individual organism is proposed and illustrated for heterotrophic organisms. This approach indicates that mass transformations can be identified by accounting for maintenance requirements and overhead costs for the various metabolic processes at the population level. The theoretical background for coupling the dynamics of the structure of communities to nutrient cycles, including the water balance, as well as explicit expressions for the dissipating heat at the population level are obtained based on the conservation law of energy. Specifications of the general theory employ the Dynamic Energy Budget model for individuals. Copyright 1999 Academic Press.

Utility of nematode community analysis as an integrated measure of the functional state of soils: perspectives and challenges

Soil nematode communities have the potential to provide unique insights into many aspects of soil processes. Since most nematodes are active in soil throughout the year, they can potentially provide a holistic measure of the biotic and functional status of soils. In contrast to other soil microbial groups, representative samples of soil nematode communities are relatively easy to obtain. However, most current nematode ecological information has been survey-based or purely observational in nature, with a persistent focus on detailed taxonomic analysis of nematode communities. The development of a Maturity Index, MI, represents a significant advance in classifying communities and it continues to be refined and developed. But, to develop a wide capacity to use soil nematode information for diagnostic and predictive purposes, particularly for agricultural soils, we need a new, more robust approach, which does not require extensive taxonomic skill and includes more functional criteria. One of the key attributes of nematodes is the relationship between structural form (principally oesophagal feeding apparatus) and function (i.e. trophic group). Nematode form is readily determinable by direct observation of extracted nematodes and high-level taxonomic skills are not needed to assign the major community components to their different trophic and ecological groups. Consequently, the trophic structure of nematode communities is relatively easy to determine and can provide an integrated measure of the status of the other groups on which they feed. Similarly, population numbers and proportions of juveniles and adults can be readily determined, permitting calculation of relative biomass and dynamics of population growth. The size distribution of individuals within the community is likely also to be an indicator of the structural status of soils from a biotic standpoint. However, fundamental gaps remain in our understanding which limit our ability to relate differences in nematode communities to functional differences. There needs to be a greater emphasis on the development and experimental testing of hypotheses, a greater integration of nematology into soil-process related studies, and the development of a specific, soil-nematode related theoretical framework for understanding epidemiological and soil colonisation processes.

Two-Sided Bounds for Ruin Probabilities when the Adjustment Coefficient does not Exist

In this paper, we derive two-sided bounds for the ruin probability in the compound Poisson risk model when the adjustment coefficient of the individual claim size distribution does not exist. These bounds also apply directly to the tails of compound geometric distributions. The upper bound is tighter than that of Dickson (1994). The corresponding lower bound, which holds under the same conditions, is tighter than that of De Vylder and Goovaerts (1984). Even when the adjustment coefficient exists, the upper bound is, in some cases, tighter than Lundberg's bound. These bounds are applicable for any positive distribution function with a finite mean. Examples are given and numerical comparisons with asymptotic formulae for the ruin probability are also considered.

Use of molecular methods to estimate the size and distribution of mycelial individuals of the ectomycorrhizal basidiomycete Pisolithus tinctorius

A field study was conduced to determine the size and spatial distribution of mycelial individuals of Pisolithus tinctorius at a site in NSW, Australia. Following collection and mapping of carpophores and isolation of the fungi into axenic culture, genomic DNA was extracted and combined data from RAPD and microsatellite analyses used to identify and map mycelial individuals. Thirty-three genetically distinct individuals were recognized at the field site and, while one large individual (at least 30 m diam.) was identified, most individuals appeared relatively small ( P. tinctorius mycelia through soil.

Predicting the spectral and broadband aerosol transmittance in the atmosphere for solar radiation modelling

Calculations of the spectral transmittance of the atmospheric aerosol, using Mie theory, for wavelengths between 0 and 40 μm is presented. The chemical composition of the aerosol particles has been modelled in order to correspond to the atmospheric conditions of medium and large coastal or near coastal cities with important industrial and other anthropogenic emission sources. Individual size distributions and optical properties for each aerosol constituent have been considered. Based on the detailed aerosol model, and using parameterization techniques, analytical broadband aerosol transmission functions for the absorption and total attenuation are obtained. The accuracy of the proposed expressions are verified with various tests, using data from the National Observatory of Athens (NOA). The proposed broadband aerosol transmission functions can be incorporated directly into solar radiation models to predict accurately the beam, diffuse and global solar radiation at a given place.