Numerical simulations of stochastic circulatory models

Properties of two of the stochastic circulatory models theoretically introduced by Smith et al., 1997, Bull. Math. Biol. 59, 1–22 were investigated. The models assumed the gamma distribution of the cycle time under either the geometric or Poisson elimination scheme. The reason for selecting these models was the fact that the probability density functions of the residence time of these models are formally similar to those of the Bateman and gamma-like function models, i.e., the two common deterministic models. Using published data, the analytical forms of the probability density functions of the residence time and the distributions of the simulated values of the residence time were determined on the basis of the deterministic models and the stochastic circulatory models, respectively. The Kolmogorov-Smirnov test revealed that even for 1000 xenobiotic particles, i.e., a relatively small number if the particles imply drug molecules, the probability density functions of the residence time based on the deterministic models closely matched the distributions of the simulated values of the residence time obtained on the basis of the stochastic circulatory models, provided that parameters of the latter models fulfilled selected conditions.     

暴露评估中样本采集量的模拟研究

选择暴露评估常用的4种右偏分布,就评估关注的高百分位数估计与采样量的关系进行模拟研究;又以对数正态分布为代表,从分布形态和变异的角度做了细致探讨.结果表明：（1）对右偏分布来说,百分位数越高,准确估计所需的采样容量就越大.而其估计值都随采样量的增大而趋近理论值,精度也随之增大,采样量500时,本文考察的4种右偏分布除P99.9外的其它百分位数都得到了较为准确的估计.（2）估计相同的百分位数,对数正态分布所需的样本容量要比正态分布大得多;而其分布变异越大,所需的采样量也就越大.本研究可为暴露评估中数据的采样调查提供借鉴.     

The many faces of population density

Population density, one of the most fundamental demographic attributes, may vary systematically with spatial scale, but this scale-sensitivity is incompletely understood. We used a novel approach—based on fully censused and mapped distributions of eastern grey squirrel (Sciurus carolinensis) dreys, beaver (Castor canadensis) lodges, and moose (Alces alces)—to explore the scale-dependence of population density and its relationship to landscape features. We identified population units at several scales, both objectively, using cluster analysis, and arbitrarily, using artificial bounds centred on high-abundance sites. Densities declined with census area. For dreys, this relationship was stronger in objective versus arbitrary population units. Drey density was inconsistently related to patch area, a relationship that was positive for all patches but negative when non-occupied patches were excluded. Drey density was negatively related to the proportion of green-space and positively related to the density of buildings or roads, relationships that were accentuated at coarser scales. Mean drey densities were more sensitive to scale when calculated as organism-weighted versus area-weighted averages. Greater understanding of these scaling effects is required to facilitate comparisons of population density across studies.     

The Curious Anomaly of Skewed Judgment Distributions and Systematic Error in the Wisdom of Crowds

Judgment distributions are often skewed and we know little about why. This paper explains the phenomenon of skewed judgment distributions by introducing the augmented quincunx (AQ) model of sequential and probabilistic cue categorization by neurons of judges. In the process of developing inferences about true values, when neurons categorize cues better than chance, and when the particular true value is extreme compared to what is typical and anchored upon, then populations of judges form skewed judgment distributions with high probability. Moreover, the collective error made by these people can be inferred from how skewed their judgment distributions are, and in what direction they tilt. This implies not just that judgment distributions are shaped by cues, but that judgment distributions are cues themselves for the wisdom of crowds. The AQ model also predicts that judgment variance correlates positively with collective error, thereby challenging what is commonly believed about how diversity and collective intelligence relate. Data from 3053 judgment surveys about US macroeconomic variables obtained from the Federal Reserve Bank of Philadelphia and the Wall Street Journal provide strong support, and implications are discussed with reference to three central ideas on collective intelligence, these being Galton''s conjecture on the distribution of judgments, Muth''s rational expectations hypothesis, and Page''s diversity prediction theorem.     

Gendist: An R Package for Generated Probability Distribution Models

In this paper, we introduce the R package gendist that computes the probability density function, the cumulative distribution function, the quantile function and generates random values for several generated probability distribution models including the mixture model, the composite model, the folded model, the skewed symmetric model and the arc tan model. These models are extensively used in the literature and the R functions provided here are flexible enough to accommodate various univariate distributions found in other R packages. We also show its applications in graphing, estimation, simulation and risk measurements.     

Intraspecific body size frequency distributions of insects

Although interspecific body size frequency distributions are well documented for many taxa, including the insects, intraspecific body size frequency distributions (IaBSFDs) are more poorly known, and their variation among mass-based and linear estimates of size has not been widely explored. Here we provide IaBSFDs for 16 species of insects based on both mass and linear estimates and large sample sizes (n ≥ 100). In addition, we review the published IaBSFDs for insects, though doing so is complicated by their under-emphasis in the literature. The form of IaBSFDs can differ substantially between mass-based and linear measures. Nonetheless, in non-social insects they tend to be normally distributed (18 of 27 species) or in fewer instances positively skewed. Negatively skewed distributions are infrequently reported and log transformation readily removes the positive skew. Sexual size dimorphism does not generally cause bimodality in IaBSFDs. The available information on IaBSFDs in the social insects suggests that these distributions are usually positively skewed or bimodal (24 of 30 species). However, only c. 15% of ant genera are polymorphic, suggesting that normal distributions are probably more common, but less frequently investigated. Although only 57 species, representing seven of the 29 orders of insects, have been considered here, it appears that whilst IaBSFDs are usually normal, other distribution shapes can be found in several species, though most notably among the social insects. By contrast, the interspecific body size frequency distribution is typically right-skewed in insects and in most other taxa.     

Densities of Two Frugivorous Primates with Respect to Forest and Fragment Tree Species Composition and Fruit Availability

Conservation of wildlife populations requires extensive knowledge of their habitat requirements, efficient methods to evaluate habitat quality, and an understanding of the value of fragments and edges. Kibale National Park, Uganda has areas that differ in the densities of 2 species of frugivorous monkeys—Cercopithecus mitis and Lophocebus albigena—including one on an edge and forest fragments outside the park that lack both species. We compared the basal area densities of important food trees with primate densities. The density of Cercopithecus mitis correlates most strongly with the basal area density of all types of food trees combined. The density of Lophocebus albigena does not correlate with the basal area densities of any category of food trees or with fruit availability. An index of their density—number of groups seen per km walked—correlates to fruit availability but with marginal significance. Lack of a relationship between the basal area densities of food trees and density of Lophocebus albigena may be the result of a mismatch in scale between the forest area measured and their large home ranges. We compared the unused area of forest to the other areas of the forest and the fragments and found it had higher basal area densities in all food tree categories for both species than the fragments and lower basal area densities of most categories than the other parts of the forest, indicating that the fragments are poor quality and would probably be unused even if dispersal were likely.     

To kill a kangaroo: understanding the decision to pursue high-risk/high-gain resources

In this paper, we attempt to understand hunter–gatherer foraging decisions about prey that vary in both the mean and variance of energy return using an expected utility framework. We show that for skewed distributions of energetic returns, the standard linear variance discounting (LVD) model for risk-sensitive foraging can produce quite misleading results. In addition to creating difficulties for the LVD model, the skewed distributions characteristic of hunting returns create challenges for estimating probability distribution functions required for expected utility. We present a solution using a two-component finite mixture model for foraging returns. We then use detailed foraging returns data based on focal follows of individual hunters in Western Australia hunting for high-risk/high-gain (hill kangaroo) and relatively low-risk/low-gain (sand monitor) prey. Using probability densities for the two resources estimated from the mixture models, combined with theoretically sensible utility curves characterized by diminishing marginal utility for the highest returns, we find that the expected utility of the sand monitors greatly exceeds that of kangaroos despite the fact that the mean energy return for kangaroos is nearly twice as large as that for sand monitors. We conclude that the decision to hunt hill kangaroos does not arise simply as part of an energetic utility-maximization strategy and that additional social, political or symbolic benefits must accrue to hunters of this highly variable prey.     

Analysis of vesicular-arbuscular mycorrhizal colonization data with a logistic regression model

 Vesicular-arbuscular mycorrhizal (VAM) infection is usually expressed as percentage of root length colonized. The frequency distributions of the data are often non-normal and may follow a negative binomial distribution. Data transformation, such as an arcsin of percentage colonization, may be used to help colonization data satisfy the normal distribution assumption, but is not always successful. In this paper, we compare ANOVA and logistic regression model (LRM) analysis of data on the effect of phosphorus fertilization and corn cultivar on VAM colonization. Transformed data did not fit a normal distribution, and we propose the LRM as a better model for statistical analysis of VAM colonization. The LRM is more accurate because (1) this model assumes a binomial distribution, (2) it incorporates the original sample size into the probability estimation, and (3) the model uses non-transformed data, which are easier to interpret. Accepted: 3 November ▪▪▪     

Seed abortion in wind-dispersed pods of Dalbergia sissoo: maternal regulation or sibling rivalry?

Summary Dalbergia sissoo, a wind-dispersed tropical tree, shows a positively skewed distribution of seeds per pod. This is attributed to the enhanced dispersal advantage of few-seeded pods due to their reduced wing loading (ratio of weight to pod surface area) and low settling velocity. The proximate mechanisms causing the positively skewed distribution were investigated. The distribution could not be attributed to the distribution pattern of ovule number per ovary, pollen grain limitation, lack of ovule fertilization, or post-fertilization elimination of many-seeded pods. Rather, it was caused by the post-fertilization abortion of seeds within a pod 2 weeks after fertilization. This intra-pod seed abortion (IPSA) is due to a dominance hierarchy of fertilized ovules from the distal (near stigma) to the basal end, generated by the temporal differences in fertilization. The dominant developing seeds at the distal end cause the abortion of others through the production and diffusion of an aborting agent. When the dominance hierarchy of the siblings is not intense, pods are formed with more than one seed. We argue that the positively skewed distribution of seeds per pod is not due to maternal regulation but is a result of sibling rivalry. We propose that this sibling rivalry is generated by genetic differences in pollen grain fitness and disucss the results in the context of parent-offspring conflict.     

Does energy availability influence classical patterns of spatial variation in exotic species richness?

Aim At macroecological scales, exotic species richness is frequently positively correlated with human population density. Such patterns are typically thought to arise because high human densities are associated with increased introduction effort and/or habitat modification and disturbance. Exotic and native species richness are also frequently positively correlated, although the causal mechanisms remain unclear. Energy availability frequently explains much of the variation in species richness and we test whether such species–energy relationships may influence the relationships of exotic species richness with human population density and native species richness. Location Great Britain. Methods We first investigate how spatial variation in the distributions of the 10 exotic bird species is related to energy availability. We then model exotic species richness using native avian species richness, human population density and energy availability as predictors. Species richness is modelled using two sets of models: one assumes independent errors and the other takes spatial correlation into account. Results The probability of each exotic species occurring, in a 10‐km quadrat, increases with energy availability. Exotic species richness is positively correlated with energy availability, human population density and native species richness in univariate tests. When taking energy availability into account, exotic species richness is negligibly influenced by human population density, but remains positively associated with native species richness. Main conclusions We provide one of the few demonstrations that energy availability exerts a strong positive influence on exotic species richness. Within our data, the positive relationship between exotic species richness and human population density probably arises because both variables increase with energy availability, and may be independent of the influence of human density on the probability of establishment. Positive correlations between exotic and native species richness remain when controlling for the influence of energy on species richness. The relevance of such a finding to the debate on the relationship between diversity and invasibility is discussed.     

Coalescence Times and FST Under a Skewed Offspring Distribution Among Individuals in a Population

Estimates of gene flow between subpopulations based on F_ST (or N_ST) are shown to be confounded by the reproduction parameters of a model of skewed offspring distribution. Genetic evidence of population subdivision can be observed even when gene flow is very high, if the offspring distribution is skewed. A skewed offspring distribution arises when individuals can have very many offspring with some probability. This leads to high probability of identity by descent within subpopulations and results in genetic heterogeneity between subpopulations even when Nm is very large. Thus, we consider a limiting model in which the rates of coalescence and migration can be much higher than for a Wright–Fisher population. We derive the densities of pairwise coalescence times and expressions for F_ST and other statistics under both the finite island model and a many-demes limit model. The results can explain the observed genetic heterogeneity among subpopulations of certain marine organisms despite substantial gene flow.     

Probability Density Function of the Red Cell Membrane Permeability Coefficient

The distribution of a random variable is determined by the probability density functions (PDF) of all other random variables with which the variable in question is jointly distributed. If the PDF of the random variable of interest is normal, or skewed normal, then the distributions with which it is jointly distributed determine its mean and standard deviation. In the case described here (where hemolysis time of the red blood cell is a function of the permeability coefficient and geometric variables of the cell) the mean and standard deviation of the permeability coefficient and the known distributions of the geometric variables on which the hemolysis time depends determine a predicted distribution of hemolysis time. An observed distribution of the hemolysis time is obtained spectrophotometrically. By choosing the mean and standard deviation of the permeability coefficient so that the predicted PDF of the hemolysis time matches the observed PDF best by least-squares criterion, the complete distribution of the permeability coefficient is determined.     

A Mathematical Model for Evolution and SETI

Darwinian evolution theory may be regarded as a part of SETI theory in that the factor f_l in the Drake equation represents the fraction of planets suitable for life on which life actually arose. In this paper we firstly provide a statistical generalization of the Drake equation where the factor f_l is shown to follow the lognormal probability distribution. This lognormal distribution is a consequence of the Central Limit Theorem (CLT) of Statistics, stating that the product of a number of independent random variables whose probability densities are unknown and independent of each other approached the lognormal distribution when the number of factors increased to infinity. In addition we show that the exponential growth of the number of species typical of Darwinian Evolution may be regarded as the geometric locus of the peaks of a one-parameter family of lognormal distributions (b-lognormals) constrained between the time axis and the exponential growth curve. Finally, since each b-lognormal distribution in the family may in turn be regarded as the product of a large number (actually “an infinity”) of independent lognormal probability distributions, the mathematical way is paved to further cast Darwinian Evolution into a mathematical theory in agreement with both its typical exponential growth in the number of living species and the Statistical Drake Equation.     

Towards malaria elimination - a new thematic series

The launch of a new thematic series of Malaria Journal -- "Towards malaria elimination" -- creates the forum that allows carrying scientific evidence on how to achieve malaria elimination in specific endemic settings and conditions into the circles of scientists, public health specialists, national and global programme managers, funders and decision makers.     

Potential Changes in the Distributions of Western North America Tree and Shrub Taxa under Future Climate Scenarios

Increases in atmospheric greenhouse gases are driving significant changes in global climate. To project potential vegetation response to future climate change, this study uses response surfaces to describe the relationship between bioclimatic variables and the distribution of tree and shrub taxa in western North America. The response surfaces illustrate the probability of the occurrence of a taxon at particular points in climate space. Climate space was defined using three bioclimatic variables: mean temperature of the coldest month, growing degree days, and a moisture index. Species distributions were simulated under present climate using observed data (1951–80, 30-year mean) and under future climate (2090–99, 10-year mean) using scenarios generated by three general circulation models—HADCM2, CGCM1, and CSIRO. The scenarios assume a 1% per year compound increase in greenhouse gases and changes in sulfate (SO₄) aerosols based on the Intergovernmental Panel on Climate Change (IPCC) IS92a scenario. The results indicate that under future climate conditions, potential range changes could be large for many tree and shrub taxa. Shifts in the potential ranges of species are simulated to occur not only northward but in all directions, including southward of the existing ranges of certain species. The simulated potential distributions of some species become increasingly fragmented under the future climate scenarios, while the simulated potential distributions of other species expand. The magnitudes of the simulated range changes imply significant impacts to ecosystems and shifts in patterns of species diversity in western North America. Received 12 May 2000; accepted 20 December 2000.     

Generalised Extreme Value Distributions Provide a Natural Hypothesis for the Shape of Seed Mass Distributions

Among co-occurring species, values for functionally important plant traits span orders of magnitude, are uni-modal, and generally positively skewed. Such data are usually log-transformed “for normality” but no convincing mechanistic explanation for a log-normal expectation exists. Here we propose a hypothesis for the distribution of seed masses based on generalised extreme value distributions (GEVs), a class of probability distributions used in climatology to characterise the impact of event magnitudes and frequencies; events that impose strong directional selection on biological traits. In tests involving datasets from 34 locations across the globe, GEVs described log10 seed mass distributions as well or better than conventional normalising statistics in 79% of cases, and revealed a systematic tendency for an overabundance of small seed sizes associated with low latitudes. GEVs characterise disturbance events experienced in a location to which individual species’ life histories could respond, providing a natural, biological explanation for trait expression that is lacking from all previous hypotheses attempting to describe trait distributions in multispecies assemblages. We suggest that GEVs could provide a mechanistic explanation for plant trait distributions and potentially link biology and climatology under a single paradigm.     

Dispersal and biogeography of silica-scaled chrysophytes

The silica-scaled chrysophytes—here mainly represented by the freshwater genera Mallomonas and Synura—have special problems in dispersal from one habitat to another because they cannot tolerate desiccation. Their dispersal is limited by the fragile construction and aquatic habit. Dispersal from one water body to another involves dangerous changes of the environment, and the ability to avoid desiccation during transport is crucial. So, air-borne and ectozoic dispersal by birds or mammals can only work at short distances. This danger may be avoided by endozoic dispersal of thick-walled cysts; as far as they can tolerate the digestion fluids in the intestine. In spite of these difficulties, Chrysophytes have been dispersed worldwide, but they display various distinct distribution patterns, e.g., cosmopolitan, arctic-northern temperate, bipolar, and tropical. Quite a large proportion may be considered endemic, occurring only within a restricted area. Even if the exact dispersal methods are elusive, the distribution of chrysophytes around the world proves their ability for dispersal. On the other hand, the different degree of distribution shows the varying success of the individual species. The distribution of a species at a given time depends on several factors: dispersal capacity—available vectors—suitable available habitats—and most important: sufficient time for dispersal. It is remarkable that the chrysophytes—in spite of their fragile cell construction and apparently low dispersal capacity—show distribution types comparable to those found in, e.g., blue–greens and desmids, whose cell construction appears much better adapted for dispersal. Special Issue: Protist diversity and geographic distribution. Guest editor: W. Foissner     

Responses of ring widths and maximum densities of Larix gmelinii to climate on contrasting north- and south-facing slopes in central Siberia

An analysis was performed of the climatic responses of the radial growth of Larix gmelinii (Rupr.) Rupr. at two sites—both of which included contrasting north- and south-facing slopes—in Tura, central Siberia, with the development of ring width and maximum-density chronologies for each slope. Both residual and standard chronologies of ring widths were positively correlated with temperature from late May until mid June on all four slopes. By contrast, standard chronologies of ring widths were negatively correlated with precipitation during the winter (from October to April) and in May on the north-facing slope at site 1 and on the south-facing slope at site 2 respectively. The negative correlations with precipitation during the winter and in May on some of the slopes suggested that delayed snowmelt in early spring might inhibit the radial growth of L. gmelinii, and the effects of snow are likely to vary with topography. Both residual and standard chronologies of maximum densities were positively correlated with temperature in early July on all four slopes. Maximum densities were also positively correlated with precipitation during summer of the previous year on all the slopes. These suggest that no major differences exist in terms of responses of maximum density to climatic factors between the north- and south-facing slopes.     

Time development of probability distributions for interacting species

A general solution to the dynamical equation for the probability distribution associated withn interacting species is obtained by employing the author's generic canonical expression for the rate functions. Interacting species models with limit-cycle dynamics and no stable equilibrium points feature probability distributions that are asymptotic for large values oft to Dirac δ-distributions concentrated on the limit-cycles, as illustrated here for an analytically solvable two-species model. For ann-species Volterra model, a stationary or temporally-averaged probability distribution should generally be much more complicated than the specialized Poisson form studied by Kerner and others.